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Xét tính đơn điệu dựa vào đạo hàm của hàm số SVIP

Câu 1 (1đ):

Cho hàm số y=f(x)y=f(x) có đồ thị như hình vẽ sau:

-1-2-3-4-51234512345-1-2-3-4-5ABCxyO

Hàm số đã cho nghịch biến trong khoảng nào dưới đây?

(−2;+∞)(-2 ; +∞).
(−2;0)(-2 ; 0 ).
(−∞;−2)(-∞ ; -2).
(0;+∞)(0 ; +∞ ).
Câu 2 (1đ):

Cho hàm số có đồ thị như sau:

-1-2-3-4-5-6-7-8-9-10-11-12123456789101112123456789101112-1-2-3-4-5-6-7-8-9-10-11-12ABxyO

Hàm số đã cho đồng biến trong khoảng nào dưới đây?

(2;+∞)(2 ; +∞ ).
(−2;2)(-2 ; 2).
(−2;+∞)(-2 ; +∞).
(−∞;2)(-∞ ; 2).
Câu 3 (1đ):

Cho hàm số y=f(x)y=f(x) có đồ thị như hình vẽ:

-1-2-3-4-5-6-712345671234567-1-2-3-4-5-6-7ABCxyO

Hàm số đã cho nghịch biến trong khoảng nào dưới đây?

(−∞;0)( -∞ ; 0 ).
(−2;2)(-2 ; 2).
(−∞;2)( -∞ ;2).
(0;+∞)(0 ; +∞ ).
Câu 4 (1đ):

Cho hàm số y=f(x)y=f(x) có bảng biến thiên như hình dưới đây

∞ ! aaaaa − + ∞ − + − + ∞ ∞ − ∞ − 0 0 4 4 7 4 x f'(x) f(x)

Mệnh đề nào sau đây sai?

Hàm số đồng biến trên khoảng (−4;4)\left(-4;4\right).
Hàm số nghịch biến trên khoảng (6;+∞)\left(6;+\infty\right).
Hàm số nghịch biến trên khoảng (4;6)\left(4 ;6\right).
Hàm số đồng biến trên khoảng (−∞;−4)\left(-\infty ; -4\right).
Câu 5 (1đ):

Cho hàm số y=f(x)y=f(x) có bảng biến thiên như hình dưới đây

∞ ! aaaaa − + ∞ − + + ∞ ∞ − 0 0 3 3 8 x f'(x) f(x) 0 0 − + + ∞ 0 0

Mệnh đề nào sau đây đúng?

Hàm số đồng biến trên khoảng (0;3)\left(0;3\right).
Hàm số nghịch biến trên khoảng (−∞;−3)\left(-\infty ; -3\right).
Hàm số đồng biến trên khoảng (−3;3)\left(-3 ;3\right).
Hàm số nghịch biến trên khoảng (−3;0)\left(-3 ; 0 \right).
Câu 6 (1đ):

Cho hàm số y=f(x)y=f(x) có bảng biến thiên như hình dưới đây

∞ ! aaaaa + ∞ − − + ∞ ∞ − ∞ − 2 4 x f'(x) f(x) 4

Mệnh đề nào sau đây đúng?

A
Hàm số nghịch biến trên (−∞;2)∪(2;+∞)\left(-\infty ;2\right) \cup \left(2;+\infty\right).
B
Hàm số nghịch biến từng khoảng (−∞;2)\left(-\infty ;2\right) và (2;+∞)\left(2;+\infty\right).
C
Hàm số đồng biến trên từng khoảng (−∞;2)\left(-\infty ;2\right) và (2;+∞)\left(2;+\infty\right).
D
Hàm số nghịch biến trên R\mathbb{R}.
Câu 7 (1đ):

Cho hàm số y=f(x)y=f(x). Hàm số y=f′(x)y=f'(x) có đồ thị như hình dưới.

-1-2-3-4-5-6123456123456-1-2-3-4-5-6xyO

Hàm số y=f(3−x)y=f(3-x) đồng biến trong khoảng nào dưới đây?

(−∞;−1)(-∞ ;-1)
(1;+∞)(1;+∞)
(−∞;2)(-∞ ;2)
(1;2)(1;2)
Câu 8 (1đ):

Hàm số y=−x2−8x−15y=-x^{2}-8x-15 nghịch biến trong khoảng nào dưới đây?

(−5;−3)(-5 ; -3).
(−4;+∞)(-4 ; +∞).
(−∞;−3)(-∞ ; -3).
(−5;+∞)(-5 ; +∞).
Câu 9 (1đ):

Cho hàm số y=f(x)y=f(x) có đạo hàm là hàm y=g(x)y = g(x). Biết hàm y=g(x)y=g(x) có đồ thị như sau:

-1-2-3-4-5-6-712345671234567-1-2-3-4-5-6-7ABCxyO

Hàm số f(x)f(x) đồng biến trong khoảng nào dưới đây?

(0;+∞)(0 ; +∞ ).
(−∞;0)( -∞ ; 0).
(−2;2)(-2 ; 2).
(−∞;−2)(-∞ ;-2).
Câu 10 (1đ):

Hàm số y=@p.bt.dsort().tex()@y=@p.bt.dsort().tex()@ @qu[p.t]@ trong khoảng nào dưới đây?

@p.o[0]@.
@p.o[2]@.
@p.o[1]@.
@p.o[3]@.

+ p.khoang[2] + '; p.o[1] = ' + p.khoang[1] + '; p.o[2] = '(′+Math.min(p.x1,p.x2)+′;+∞);p.o[3]=′(' + Math.min(p.x1, p.x2) + ' ; +∞); p.o[3] = '(-&#8734 ; ' + Math.max(p.x1, p.x2) + '); } else if ((p.a > 0 && p.t ==1) || (p.a < 0 && p.t ==0)) { p.o[0] = ' + p.khoang[1] + '; p.o[1] = ' + p.khoang[0] + '; p.o[2] = '(′+Math.min(p.x1,p.x2)+′;+∞);p.o[3]=′(' + Math.min(p.x1, p.x2) + ' ; +∞); p.o[3] = '(-&#8734 ; ' + Math.max(p.x1, p.x2) + '); } function f1(x){return x*x}; function bbt3(type,bien){ var x1 = bien[0], x2 = bien[2], y1 = bien[1], y2 = bien[3]; switch(type){ case 1: // hàm bậc 3 có y` >= 0, y = 0 tại x = 0 return '<svg width="453" height="192" xmlns="http://www.w3.org/2000/svg"> <line stroke="#000" stroke-linecap="undefined" stroke-linejoin="undefined" id="svg_1" y2="174.25423" x2="89" y1="23.24996" x1="89" stroke-width="1.5" fill="none"/> <line stroke="#000" stroke-linecap="undefined" stroke-linejoin="undefined" id="svg_2" y2="60.24955" x2="394.01381" y1="60.24955" x1="49.99922" fill-opacity="null" stroke-opacity="null" stroke-width="1.5" fill="none"/> <line stroke="#000" stroke-linecap="undefined" stroke-linejoin="undefined" id="svg_3" y2="100.24968" x2="394.01381" y1="100.24968" x1="49.99922" fill-opacity="null" stroke-opacity="null" stroke-width="1.5" fill="none"/> <line stroke-linecap="undefined" stroke-linejoin="undefined" id="svg_14" y2="110.24971" x2="358.00022" y1="169.2499" x1="124.99947" fill-opacity="null" stroke-opacity="null" stroke-width="1.5" stroke="#000" fill="none"/> <text xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_4" y="52.24953" x="60.99927" fill-opacity="null" stroke-opacity="null" stroke-width="0" stroke="#000" fill="#000000">x</text> <text xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_5" y="90.24965" x="60.99927" fill-opacity="null" stroke-opacity="null" stroke-width="0" stroke="#000" fill="#000000">y&apos;</text> <text xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_6" y="139.24981" x="60.99927" fill-opacity="null" stroke-opacity="null" stroke-width="0" stroke="#000" fill="#000000">y</text> <text stroke="#000" xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_7" y="52.24953" x="100.9994" fill-opacity="null" stroke-opacity="null" stroke-width="0" fill="#000000">-∞</text> <text stroke="#000" xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_8" y="52.24953" x="365.00025" fill-opacity="null" stroke-opacity="null" stroke-width="0" fill="#000000">+∞</text> <text stroke="#000" xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_10" y="53.24953" x="230.99982" fill-opacity="null" stroke-opacity="null" stroke-width="0" fill="#000000">0</text> <text stroke="#000" xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_11" y="92.24966" x="230.99982" fill-opacity="null" stroke-opacity="null" stroke-width="0" fill="#000000">0</text> <text stroke="#000" xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_12" y="174.24992" x="98.99939" fill-opacity="null" stroke-opacity="null" stroke-width="0" fill="#000000">-∞</text> <text stroke="#000" xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_13" y="116.24973" x="365.00025" fill-opacity="null" stroke-opacity="null" stroke-width="0" fill="#000000">+∞</text> <text transform="rotate(-20 354.5,110.73437500000006) " xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_15" y="118.24974" x="348.00019" fill-opacity="null" stroke-opacity="null" stroke="#000" fill="#000000">&gt;</text> <text stroke="#000" xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_16" y="92.24966" x="160.99959" fill-opacity="null" stroke-opacity="null" stroke-width="0" fill="#000000">+</text> <text stroke="#000" xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_17" y="92.24966" x="303.00005" fill-opacity="null" stroke-opacity="null" stroke-width="0" fill="#000000">+</text> </svg>'; case 11: // hàm bậc 3 có y` > 0 mọi x return '<svg width="453" height="192" xmlns="http://www.w3.org/2000/svg"> <line fill="none" stroke-width="1.5" x1="89" y1="23.24996" x2="89" y2="174.25423" id="svg_1" stroke-linejoin="undefined" stroke-linecap="undefined" stroke="#000"/> <line fill="none" stroke-width="1.5" stroke-opacity="null" fill-opacity="null" x1="49.99922" y1="60.24955" x2="394.01381" y2="60.24955" id="svg_2" stroke-linejoin="undefined" stroke-linecap="undefined" stroke="#000"/> <line fill="none" stroke-width="1.5" stroke-opacity="null" fill-opacity="null" x1="49.99922" y1="100.24968" x2="394.01381" y2="100.24968" id="svg_3" stroke-linejoin="undefined" stroke-linecap="undefined" stroke="#000"/> <line fill="none" stroke="#000" stroke-width="1.5" stroke-opacity="null" fill-opacity="null" x1="124.99947" y1="169.2499" x2="358.00022" y2="110.24971" id="svg_14" stroke-linejoin="undefined" stroke-linecap="undefined"/> <text fill="#000000" stroke="#000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="60.99927" y="52.24953" id="svg_4" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve">x</text> <text fill="#000000" stroke="#000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="60.99927" y="90.24965" id="svg_5" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve">y&apos;</text> <text fill="#000000" stroke="#000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="60.99927" y="139.24981" id="svg_6" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve">y</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="100.9994" y="52.24953" id="svg_7" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">-∞</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="365.00025" y="52.24953" id="svg_8" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">+∞</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="98.99939" y="174.24992" id="svg_12" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">-∞</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="365.00025" y="116.24973" id="svg_13" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">+∞</text> <text fill="#000000" stroke="#000" stroke-opacity="null" fill-opacity="null" x="348.00019" y="118.24974" id="svg_15" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" transform="rotate(-20 354.5,110.73437500000006) ">&gt;</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="230.99959" y="92.24966" id="svg_16" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">+</text> </svg>'; case 2: // hàm bậc 3 có y` <=0, y = 0 tại x = 0 return '<svg width="453" height="192" xmlns="http://www.w3.org/2000/svg"> <line fill="none" stroke-width="1.5" x1="89" y1="23.24996" x2="89" y2="174.25423" id="svg_1" stroke-linejoin="undefined" stroke-linecap="undefined" stroke="#000"/> <line fill="none" stroke-width="1.5" stroke-opacity="null" fill-opacity="null" x1="49.99922" y1="60.24955" x2="394.01381" y2="60.24955" id="svg_2" stroke-linejoin="undefined" stroke-linecap="undefined" stroke="#000"/> <line fill="none" stroke-width="1.5" stroke-opacity="null" fill-opacity="null" x1="49.99922" y1="100.24968" x2="394.01381" y2="100.24968" id="svg_3" stroke-linejoin="undefined" stroke-linecap="undefined" stroke="#000"/> <text fill="#000000" stroke="#000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="60.99927" y="52.24953" id="svg_4" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve">x</text> <text fill="#000000" stroke="#000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="60.99927" y="90.24965" id="svg_5" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve">y&apos;</text> <text fill="#000000" stroke="#000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="60.99927" y="139.24981" id="svg_6" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve">y</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="100.9994" y="52.24953" id="svg_7" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">-∞</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="365.00025" y="52.24953" id="svg_8" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">+∞</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="230.99982" y="53.24953" id="svg_10" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">0</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="230.99982" y="92.24966" id="svg_11" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">0</text> <text style="cursor: move;" fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="98.99939" y="116.24992" id="svg_12" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">+∞</text> <text style="cursor: move;" fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="365.00025" y="166.24973" id="svg_13" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">-∞</text> <text fill="#000000" stroke="#000" stroke-opacity="null" fill-opacity="null" x="351.00019" y="169.24974" id="svg_15" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" transform="rotate(13 357.5000000000002,161.734375) ">&gt;</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="160.99959" y="90.24966" id="svg_16" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">-</text> <text style="cursor: move;" fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="303.00005" y="90.24966" id="svg_17" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">-</text> <line stroke-linecap="undefined" stroke-linejoin="undefined" id="svg_9" y2="162.4375" x2="361" y1="110.4375" x1="132" fill-opacity="null" stroke-opacity="null" stroke-width="1.5" stroke="#000" fill="none"/> </svg>'; case 21: // hàm bậc 3 có y` < 0 mọi x return '<svg width="453.00000000000006" height="192" xmlns="http://www.w3.org/2000/svg"> <line stroke="#000" stroke-linecap="undefined" stroke-linejoin="undefined" id="svg_1" y2="174.25423" x2="89" y1="23.24996" x1="89" stroke-width="1.5" fill="none"/> <line stroke="#000" stroke-linecap="undefined" stroke-linejoin="undefined" id="svg_2" y2="60.24955" x2="394.01381" y1="60.24955" x1="49.99922" fill-opacity="null" stroke-opacity="null" stroke-width="1.5" fill="none"/> <line stroke="#000" stroke-linecap="undefined" stroke-linejoin="undefined" id="svg_3" y2="100.24968" x2="394.01381" y1="100.24968" x1="49.99922" fill-opacity="null" stroke-opacity="null" stroke-width="1.5" fill="none"/> <text xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_4" y="52.24953" x="60.99927" fill-opacity="null" stroke-opacity="null" stroke-width="0" stroke="#000" fill="#000000">x</text> <text xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_5" y="90.24965" x="60.99927" fill-opacity="null" stroke-opacity="null" stroke-width="0" stroke="#000" fill="#000000">y&apos;</text> <text xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_6" y="139.24981" x="60.99927" fill-opacity="null" stroke-opacity="null" stroke-width="0" stroke="#000" fill="#000000">y</text> <text stroke="#000" xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_7" y="52.24953" x="100.9994" fill-opacity="null" stroke-opacity="null" stroke-width="0" fill="#000000">-∞</text> <text stroke="#000" xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_8" y="52.24953" x="365.00025" fill-opacity="null" stroke-opacity="null" stroke-width="0" fill="#000000">+∞</text> <text stroke="#000" xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_12" y="174.24992" x="368.16606" fill-opacity="null" stroke-opacity="null" stroke-width="0" fill="#000000">-∞</text> <text stroke="#000" xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_13" y="116.24973" x="95.00025" fill-opacity="null" stroke-opacity="null" stroke-width="0" fill="#000000">+∞</text> <text transform="rotate(13 357.5833740234375,168.23439025878906) " xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_15" y="175.74974" x="351.33352" fill-opacity="null" stroke-opacity="null" stroke="#000" fill="#000000">&gt;</text> <text stroke="#000" xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_16" y="92.24966" x="230.99959" fill-opacity="null" stroke-opacity="null" stroke-width="0" fill="#000000">-</text> <line stroke-linecap="undefined" stroke-linejoin="undefined" id="svg_9" y2="169.4375" x2="362" y1="111.4375" x1="127" fill-opacity="null" stroke-opacity="null" stroke-width="1.5" stroke="#000" fill="none"/> </svg>'; case 3: // hàm bậc 3, a> 0 y` có hai nghiệm return '<svg width="504.00000000000006" height="192" xmlns="http://www.w3.org/2000/svg"> <line fill="none" stroke-width="1.5" x1="89" y1="23.24996" x2="89" y2="184.73045" id="svg_1" stroke-linejoin="undefined" stroke-linecap="undefined" stroke="#000"/> <line fill="none" stroke-width="1.5" stroke-opacity="null" fill-opacity="null" x1="49.99922" y1="60.24955" x2="473.06155" y2="60.24955" id="svg_2" stroke-linejoin="undefined" stroke-linecap="undefined" stroke="#000"/> <line fill="none" stroke-width="1.5" stroke-opacity="null" fill-opacity="null" x1="49.99922" y1="100.24968" x2="474.014" y2="100.24968" id="svg_3" stroke-linejoin="undefined" stroke-linecap="undefined" stroke="#000"/> <line fill="none" stroke="#000" stroke-width="1.5" stroke-opacity="null" fill-opacity="null" x1="130.57142" y1="169.7502" x2="217.23832" y2="121.17864" id="svg_21" stroke-linejoin="undefined" stroke-linecap="undefined"/> <line stroke-linecap="undefined" stroke-linejoin="undefined" id="svg_9" y2="171.24703" x2="328.66689" y1="115.4375" x1="260.09586" fill-opacity="null" stroke-opacity="null" stroke-width="1.5" fill="none" stroke="#000"/> <line stroke="#000" fill="none" stroke-width="1.5" stroke-opacity="null" fill-opacity="null" x1="370.57142" y1="171.7502" x2="441.23832" y2="125.17864" id="svg_17" stroke-linejoin="undefined" stroke-linecap="undefined"/> <text fill="#000000" stroke="#000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="60.99927" y="52.24953" id="svg_4" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve">x</text> <text fill="#000000" stroke="#000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="60.99927" y="90.24965" id="svg_5" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve">y&apos;</text> <text fill="#000000" stroke="#000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="60.99927" y="139.24981" id="svg_6" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve">y</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="100.9994" y="52.24953" id="svg_7" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">-∞</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="439.28616" y="52.24953" id="svg_8" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">+∞</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="220.5236" y="89.39251" id="svg_11" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">0</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="442.99939" y="116.24992" id="svg_12" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">+∞</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="99.76237" y="183.63071" id="svg_13" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">-∞</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="168.30122" y="87.28673" id="svg_16" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">+</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="221.47599" y="53.24953" id="svg_10" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">'+ x1 +'</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="221.47599" y="119.91653" id="svg_19" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">'+ y1 +'</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="345.28583" y="53.24953" id="svg_14" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">'+ x2 +'</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="343.28583" y="180.0116" id="svg_20" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">'+ y2 +'</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="345.28583" y="88.48772" id="svg_18" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">0</text> <text transform="rotate(-35 213.90429687499997,122.12055969238281) " fill="#000000" stroke="#000" stroke-opacity="null" fill-opacity="null" x="207.71448" y="129.7501" id="svg_22" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve">&gt;</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="292.00367" y="87.28673" id="svg_25" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">-</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="409.78025" y="87.28673" id="svg_26" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">+</text> <text fill="#000000" stroke="#000" stroke-opacity="null" fill-opacity="null" x="320.57184" y="177.10689" id="svg_15" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" transform="rotate(39 327.0624999999999,169.59375000000006) ">&gt;</text> <text transform="rotate(-35 439.20312499999994,126.25) " fill="#000000" stroke="#000" stroke-opacity="null" fill-opacity="null" x="432.71448" y="133.7501" id="svg_23" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve">&gt;</text> </svg>'; case 4: // hàm bậc 3, a< 0 y` có hai nghiệm return '<svg width="504.00000000000006" height="192" xmlns="http://www.w3.org/2000/svg"> <line stroke="#000" stroke-linecap="undefined" stroke-linejoin="undefined" id="svg_1" y2="184.73045" x2="89" y1="23.24996" x1="89" stroke-width="1.5" fill="none"/> <line stroke="#000" stroke-linecap="undefined" stroke-linejoin="undefined" id="svg_2" y2="60.24955" x2="473.06155" y1="60.24955" x1="49.99922" fill-opacity="null" stroke-opacity="null" stroke-width="1.5" fill="none"/> <line stroke="#000" stroke-linecap="undefined" stroke-linejoin="undefined" id="svg_3" y2="100.24968" x2="474.014" y1="100.24968" x1="49.99922" fill-opacity="null" stroke-opacity="null" stroke-width="1.5" fill="none"/> <line stroke="#000" fill="none" stroke-width="1.5" stroke-opacity="null" fill-opacity="null" x1="132" y1="110.4375" x2="209.57103" y2="166.24703" id="svg_9" stroke-linejoin="undefined" stroke-linecap="undefined"/> <line stroke-linecap="undefined" stroke-linejoin="undefined" id="svg_21" y2="121.17864" x2="337.23832" y1="169.7502" x1="250.57142" fill-opacity="null" stroke-opacity="null" stroke-width="1.5" stroke="#000" fill="none"/> <line stroke="#000" fill="none" stroke-width="1.5" stroke-opacity="null" fill-opacity="null" x1="370.09586" y1="110.4375" x2="447.66689" y2="166.24703" id="svg_24" stroke-linejoin="undefined" stroke-linecap="undefined"/> <text xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_4" y="52.24953" x="60.99927" fill-opacity="null" stroke-opacity="null" stroke-width="0" stroke="#000" fill="#000000">x</text> <text xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_5" y="90.24965" x="60.99927" fill-opacity="null" stroke-opacity="null" stroke-width="0" stroke="#000" fill="#000000">y&apos;</text> <text xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_6" y="139.24981" x="60.99927" fill-opacity="null" stroke-opacity="null" stroke-width="0" stroke="#000" fill="#000000">y</text> <text stroke="#000" xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_7" y="52.24953" x="100.9994" fill-opacity="null" stroke-opacity="null" stroke-width="0" fill="#000000">-∞</text> <text stroke="#000" xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_8" y="52.24953" x="439.28616" fill-opacity="null" stroke-opacity="null" stroke-width="0" fill="#000000">+∞</text> <text stroke="#000" xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_11" y="89.39251" x="220.5236" fill-opacity="null" stroke-opacity="null" stroke-width="0" fill="#000000">0</text> <text stroke="#000" xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_12" y="116.24992" x="98.99939" fill-opacity="null" stroke-opacity="null" stroke-width="0" fill="#000000">+∞</text> <text stroke="#000" xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_13" y="185" x="449.76237" fill-opacity="null" stroke-opacity="null" stroke-width="0" fill="#000000">-∞</text> <text transform="rotate(39 207.66928100585926,164.47988891601562) " xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_15" y="172.10689" x="201.47598" fill-opacity="null" stroke-opacity="null" stroke="#000" fill="#000000">&gt;</text> <text stroke="#000" xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_16" y="87.28673" x="168.30122" fill-opacity="null" stroke-opacity="null" stroke-width="0" fill="#000000">-</text> <text stroke="#000" xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_10" y="53.24953" x="221.47599" fill-opacity="null" stroke-opacity="null" stroke-width="0" fill="#000000">'+ x1 +'</text> <text stroke="#000" xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_19" y="185.91653" x="210.47599" fill-opacity="null" stroke-opacity="null" stroke-width="0" fill="#000000">'+ y1 +'</text> <text stroke="#000" xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_14" y="53.24953" x="345.28583" fill-opacity="null" stroke-opacity="null" stroke-width="0" fill="#000000">'+ x2 +'</text> <text stroke="#000" xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_20" y="118.0116" x="345.28583" fill-opacity="null" stroke-opacity="null" stroke-width="0" fill="#000000">'+ y2 +'</text> <text stroke="#000" xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_18" y="88.48772" x="345.28583" fill-opacity="null" stroke-opacity="null" stroke-width="0" fill="#000000">0</text> <text transform="rotate(-35 333.90429687500006,122.1205596923829) " xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_22" y="129.7501" x="327.71448" fill-opacity="null" stroke-opacity="null" stroke="#000" fill="#000000">&gt;</text> <text transform="rotate(39 445.76513671875006,164.47988891601568) " xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_23" y="172.10689" x="439.57184" fill-opacity="null" stroke-opacity="null" stroke="#000" fill="#000000">&gt;</text> <text stroke="#000" xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_25" y="87.28673" x="280.00367" fill-opacity="null" stroke-opacity="null" stroke-width="0" fill="#000000">+</text> <text stroke="#000" xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_26" y="87.28673" x="409.78025" fill-opacity="null" stroke-opacity="null" stroke-width="0" fill="#000000">-</text> </svg>'; }; }

Câu 11 (1đ):

Hàm số y=14x4−12x2+4y=\frac{1}{4}x^{4}-\frac{1}{2}x^{2}+4 nghịch biến trong khoảng nào dưới đây?

(0;1)(0 ; 1)
(−1;+∞)(-1 ; +∞)
(1;+∞)(1 ; +∞)
(−∞;1)(-∞ ; 1)
Câu 12 (1đ):

Cho hàm số y=3x−53x−9y=\frac{3x-5}{3x-9}. Khẳng định nào sau đây đúng?

Hàm số nghịch biến trên khoảng (3;+∞)(3 ; +∞ ).
Hàm số nghịch biến trên khoảng (53;+∞)(\dfrac{5}{3} ; +∞ ).
Hàm số nghịch biến trên khoảng (0;+∞)(0 ; +∞).
Hàm số nghịch biến trên khoảng (−∞;+∞)(-∞ ; +∞ ).
Câu 13 (1đ):

Trong các hàm số sau, hàm số nào nghịch biến trên khoảng (−2;2)(-2;2)?

y=−1xy=\dfrac{-1}{x}.
y=1xy=\dfrac{1}{x}.
y=x3−12x+1y=x^3-12x + 1.
y=1x2y=\dfrac{1}{x^2}.
Câu 14 (1đ):

Hàm số y=x2−5x+25x−5y=\dfrac{x^2-5x+25}{x-5} đồng biến trên khoảng nào trong các khoảng cho sau đây?

(5;10)(5 ; 10).
(−∞;5)(-∞ ;5).
(0;10)(0 ;10).
(10;+∞)(10 ;+ ∞).
Câu 15 (1đ):

Cho hàm số y=4xx2−81y=\dfrac{4x}{x^2-81}. Mệnh đề nào sau đây đúng?

A
Hàm số nghịch biến trên (−∞;+∞)(-∞ ; +∞).
B
Hàm số nghịch biến trên các khoảng (−∞;−9)(-∞ ; -9) và (9;+∞)(9; +∞).
C
Hàm số nghịch biến trên (−9;9)(-9; 9).
D
Hàm số nghịch biến trên từng khoảng xác định của nó.
Câu 16 (1đ):

Hàm số nào sau đây nghịch biến trong khoảng (0;π2)\left(0;\dfrac{\pi}{2}\right) ?

y=x−cos⁡xy=x-\cos x.
y=x−cot⁡xy=x-\cot x.
y=x−tan⁡xy=x-\tan x.
y=x−sin⁡xy=x-\sin x.
Câu 17 (1đ):

Hàm số y=@p.bt.dsort().tex()@y=@p.bt.dsort().tex()@ @qu[p.t]@ trong khoảng nào dưới đây?

@p.o[2]@.
@p.o[3]@.
@p.o[0]@.
@p.o[1]@.
: '[' + Math.min(p.x1,p.x2) + ' ; ' + Math.max(p.x1,p.x2) + ']'); p.o = [",",","]; if ( p.a > 0 && p.t ==0) { p.o[0] = '$(' + Math.max(p.x1, p.x2) + ' ; +&#8734); p.o[1] = '$(' + getDigits(-p.b/(2*p.a)) + ' ; +&#8734); p.o[2] = '$(-&#8734 ;' + Math.min(p.x1, p.x2) + '); p.o[3] = '$(' + Math.min(p.x1,p.x2) + ' ; ' + Math.max(p.x1, p.x2)+ '); } else if ( p.a > 0 && p.t ==1) { p.o[0] = '$(-&#8734 ; ' + Math.min(p.x1, p.x2) + '); p.o[1] = '$(-&#8734 ; ' + getDigits(-p.b/(2*p.a)) + '); p.o[2] = '$(' + Math.max(p.x1, p.x2) + ' ; +&#8734); p.o[3] = '$(' + Math.min(p.x1,p.x2) + ' ; ' + Math.max(p.x1, p.x2)+ '); } else if ( p.a < 0 && p.t ==0) { p.o[0] = '$(' + Math.min(p.x1, p.x2) + ' ; ' + getDigits(-p.b/(2*p.a)) + '); p.o[1] = '$(-&#8734 ; ' + getDigits(-p.b/(2*p.a)) + '); p.o[2] = '$(' + Math.max(p.x1, p.x2) + ' ; +&#8734); p.o[3] = '$(' + Math.min(p.x1,p.x2) + ' ; ' + Math.max(p.x1, p.x2)+ '); } else if ( p.a < 0 && p.t ==1) { p.o[0] = '$(' + getDigits(-p.b/(2*p.a))+ ' ; ' + Math.max(p.x1, p.x2) + '); p.o[1] = '$(' + getDigits(-p.b/(2*p.a)) + ' ; +&#8734); p.o[2] = '$(-&#8734 ;' + Math.min(p.x1, p.x2) + '); p.o[3] = '$(' + Math.min(p.x1,p.x2) + ' ; ' + Math.max(p.x1, p.x2)+ '); } p.bbt = function(ty,x0,x1,x2) { if (ty ==0) { return '<svg width="590" height="192" xmlns="http://www.w3.org/2000/svg"> <rect stroke="#000" id="svg_37" height="114" width="135" y="61.2375" x="209.5" stroke-opacity="null" stroke-width="1.5" fill="#999999"/> <line fill="none" stroke-width="1.5" x1="89" y1="23.24996" x2="89" y2="174.25423" id="svg_1" stroke-linejoin="undefined" stroke-linecap="undefined" stroke="#000"/> <line stroke="#000" fill="none" stroke-width="1.5" stroke-opacity="null" fill-opacity="null" x1="49.99922" y1="60.24955" x2="479.01381" y2="60.24955" id="svg_2" stroke-linejoin="undefined" stroke-linecap="undefined"/> <line stroke="#000" fill="none" stroke-width="1.5" stroke-opacity="null" fill-opacity="null" x1="49.99922" y1="100.24968" x2="477.01377" y2="100.24968" id="svg_3" stroke-linejoin="undefined" stroke-linecap="undefined"/> <text fill="#000000" stroke="#000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="60.99927" y="52.24953" id="svg_4" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve">x</text> <text fill="#000000" stroke="#000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="60.99927" y="90.24965" id="svg_5" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve">y\'</text> <text fill="#000000" stroke="#000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="60.99927" y="139.24981" id="svg_6" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve">y</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="100.9994" y="52.24953" id="svg_7" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">-∞</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="455.00025" y="52.24953" id="svg_8" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">+∞</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="190.99982" y="52.24953" id="svg_10" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">'+ x1 + '</text> <text transform="rotate(29 176.39843750000014,158.63281249999997) " fill="#000000" stroke="#000" stroke-opacity="null" fill-opacity="null" x="170.00019" y="166.24974" id="svg_15" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve">&gt;</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="353.99939" y="176.24992" id="svg_24" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">0</text> <text transform="rotate(-22 449.39843749999994,123.63281249999991) " fill="#000000" stroke="#000" stroke-opacity="null" fill-opacity="null" x="443.00019" y="131.24974" id="svg_28" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve">&gt;</text> <line stroke-linecap="null" stroke-linejoin="null" id="svg_30" y2="82.0375" x2="155.8" y1="82.0375" x1="145.8" fill-opacity="null" stroke-opacity="null" stroke="#000" fill="none"/> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="342.99982" y="52.24953" id="svg_31" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">' + x2 + '</text> <text style="cursor: move;" stroke="#000" fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="263.99982" y="51.24953" id="svg_32" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve">' + x0 +'</text> <text xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_33" y="87.2375" x="375.5" fill-opacity="null" stroke-opacity="null" stroke-width="0" stroke="#000" fill="#000000">+</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="186.99939" y="175.24992" id="svg_36" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">0</text> <line stroke="#000" stroke-linecap="undefined" stroke-linejoin="undefined" id="svg_41" y2="123.2375" x2="451.5" y1="157.2375" x1="377.5" fill-opacity="null" stroke-opacity="null" stroke-width="1.5" fill="none"/> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="455.00025" y="118.24953" id="svg_42" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">+∞</text> <text fill="#000000" stroke-width="0" stroke-opacity="null" 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stroke="#000" stroke-linecap="undefined" stroke-linejoin="undefined" id="svg_35" y2="130.2375" x2="255.5" y1="159.2375" x1="198.5" fill-opacity="null" stroke-opacity="null" stroke-width="1.5" fill="none"/> <text fill="#000000" stroke-width="0" stroke-opacity="null" fill-opacity="null" x="185.99939" y="175.24992" id="svg_36" font-size="22" font-family="Katex_Math, Times, serif" text-anchor="start" xml:space="preserve" stroke="#000">0</text> <text xml:space="preserve" text-anchor="start" font-family="Katex_Math, Times, serif" font-size="22" id="svg_40" y="119.2375" x="255.5" fill-opacity="null" stroke-opacity="null" stroke-width="0" stroke="#000" fill="#000000">y(' + x0 + ')</text> </svg>'; } }
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