Trắc nghiệm Đạo hàm cấp hai Toán Lớp 11

A. \( \frac{{2\left( {{x^3} +3{x^2} + 93x - 77} \right)}}{{{{\left( {{x^2} - 2x - 3} \right)}^4}}}\)

B. \( \frac{{2\left( {7{x^3} - 15{x^2} + 93x - 77} \right)}}{{{{\left( {{x^2} - 2x - 3} \right)}^3}}}\)

C. \( \frac{{2\left( {{x^3} +3{x^2} + 93x - 77} \right)}}{{{{\left( {{x^2} - 2x - 3} \right)}^3}}}\)

D. \( \frac{{2\left( {7{x^3} - 15{x^2} + 93x - 77} \right)}}{{{{\left( {{x^2} - 2x - 3} \right)}^4}}}\)

A. \(\frac{2}{{{{\left( {x - 1} \right)}^4}}}\)

B. \(-\frac{2}{{{{\left( {x - 1} \right)}^3}}}\)

C. \(-\frac{2}{{{{\left( {x - 1} \right)}^4}}}\)

D. \(\frac{2}{{{{\left( {x - 1} \right)}^3}}}\)

A. \(\frac{2}{{{{\left( {x - 3} \right)}^3}}}\)

B. \(-\frac{2}{{{{\left( {x - 3} \right)}^3}}}\)

C. \(\frac{1}{{{{\left( {x - 3} \right)}^3}}}\)

D. \(-\frac{1}{{{{\left( {x - 3} \right)}^3}}}\)

A. \( \frac{2}{{{x^4}}}\)

B. \(- \frac{2}{{{x^4}}}\)

C. \(- \frac{2}{{{x^3}}}\)

D. \( \frac{2}{{{x^3}}}\)

A. \(y'' = 16{x^3} - 6x+1\)

B. \(y'' = 16{x^3} - 6\)

C. \(y'' = 4{x^3} - 6\)

D. \(y'' = -4{x^3} - 6\)

A. \(y'' = - 36{x^2} + 24x + 10\)

B. \(y'' = - 36{x^2} + 24x -10\)

C. \(y'' = - 12{x^2} + 2x + 10\)

D. \(y'' = 12{x^2} + 2x + 10\)

A. 5

B. 12

C. 8

D. 10

A. \(y''=-\frac{2 x^{3}+3 x}{\left(1+x^{2}\right) \sqrt{1+x^{2}}}\)

B. \(y''=\frac{2 x^{3}+3 x}{\left(1+x^{2}\right) \sqrt{1+x^{2}}}\)

C. \(y''=\frac{x^{3}+3 x}{\left(1+x^{2}\right) \sqrt{1+x^{2}}}\)

D. \(y''=-\frac{ x^{3}+3 x}{\left(1+x^{2}\right) \sqrt{1+x^{2}}}\)

A. \(y''=\frac{1}{(2 x+5) \sqrt{2 x+5}}\)

B. \(y''=\frac{1}{(2 x+5)^2 \sqrt{2 x+5}}\)

C. \(y''=-\frac{1}{(2 x+5) \sqrt{2 x+5}}\)

D. \(y''=\frac{1}{(2 x+5) 3\sqrt{2 x+5}}\)

A. \(y^{\prime \prime}=-\frac{2}{(x+1)^{3}}\)

B. \(y^{\prime \prime}=\frac{3}{(x+1)^{3}}\)

C. \(y^{\prime \prime}=\frac{2}{(x+1)^{2}}\)

D. \(y^{\prime \prime}=\frac{-2}{(x+1)^{2}}\)

A. \(y''=\frac{4}{(x-2)^{3}}\)

B. \(y''=\frac{2}{(x-2)^{3}}\)

C. \(y''=\frac{3}{(x-2)^{3}}\)

D. \(y''=\frac{1}{(x-2)^{3}}\)

A. \(y^{\prime \prime}= x^{4}+36 x^{2}+6\)

B. \(y^{\prime \prime}=30 x^{4}+36 x^{2}+6\)

C. \(y^{\prime \prime}=30 x^{4}-6 x^{2}+6\)

D. \(y^{\prime \prime}=30 x^{4}+36 x^{2}\)

A. \([-1 ; 2] .\)

B. \((-\infty ; 0] .\)

C. \(\varnothing\)

D. \(\{-1\}\)

A. \(y^{\prime \prime}+y=-2 \cos x .\)

B. \(y^{\prime \prime}-y^{\prime}=2 \cos x . \)

C. \( y^{\prime \prime}+y^{\prime}=2 \cos x .\)

D. \(y^{\prime \prime}+y=2 \cos x .\)

A. \(y^{\prime \prime}=\frac{2}{(1-x)^{4}} . \)

B. \(y^{\prime \prime}=\frac{2}{(1-x)^{3}} .\)

C. \( y^{\prime \prime}=2+\frac{1}{(1-x)^{2}} . \)

D. \(y^{\prime \prime}=\frac{-2}{(1-x)^{3}}\)

A. \(\begin{array}{llll} -4 \cos 2 x \end{array}\)

B. \(4 \cos 2 x\)

C. \(-2 \sin 2 x \)

D. \(-4 \sin 2 x\)

A. \(-\sqrt{2}\)

B. 1

C. 0

D. \(\sqrt{2}\)

A. \(\begin{array}{llll} \frac{80}{27} \end{array}\)

B. \(-\frac{80}{27} . \)

C. 1

D. -1

A. \(\begin{array}{llll} 16 x^{3}+6 x \end{array}\)

B. \(4 x^{3}-6 \)

C. \(16 x^{3}-6\)

D. \( 16 x^{2}-6\)

A. \(x=0, x=\frac{\pi}{3} . \)

B. \( x=\frac{\pi}{2} . \)

C. \(x=0, x=\frac{\pi}{2} .\)

D. \(x=0, x=\frac{\pi}{6}\)

A. -8

B. 17

C. 0

D. -5

A. \(\begin{aligned} &y^{2}+\left(y^{\prime}\right)^{2}=4 . \end{aligned}\)

B. \(4 y+y^{\prime \prime}=0\)

C. \(4 y-y^{\prime \prime}=0\)

D. \( y=y^{\prime} \tan 2 x\)

A. \(\begin{aligned} &\frac{2 \tan x}{\cos ^{2} x}-\frac{2 \cot x}{\sin ^{2} x}-\sin x+\cos x \end{aligned}\)

B. 0

C. \(\tan ^{2} x-\cot ^{2} x+\cos x-\sin x .\)

D. \(\frac{2 \tan x}{\cos ^{2} x}+\frac{2 \cot x}{\sin ^{2} x}-\sin x-\cos x\)

A. \(\begin{aligned} &y^{\prime \prime \prime}=\sin \left(x+\frac{3 \pi}{2}\right) . \end{aligned}\)

B. \(y^{\prime}=\sin \left(x+\frac{\pi}{2}\right)\)

C. \(y^{\prime \prime}=\sin (x+\pi)\)

D. \( y^{(4)}=\sin (2 \pi-x) \text { . }\)

A. \(-\frac{3}{4}\)

B. \(\frac{3}{4}\)

C. 1

D. -1

A. -10

B. -120

C. 10

D. 120

A. 2

B. 3

C. 4

D. 5

A. \(f^{\prime}(2)<0 .\)

B. \(f^{\prime \prime \prime}(2)<0 . \)

C. \(f^{(4)}(2)<0 . \)

D. \( f^{\prime \prime}(2)>0 .\)

A. \(\cos ^{2} 2 x .\)

B. \(-\cos ^{2} 2 x . \)

C. \(8 \cos 2 x .\)

D. \(-8 \cos 2 x .\)

A. \(\begin{aligned} &\frac{2\left(7 x^{3}+15 x^{2}-93 x+77\right)}{\left(x^{2}-2 x-3\right)^{3}} \end{aligned}\)

B. \(\frac{2\left(7 x^{3}-15 x^{2}+93 x-77\right)}{\left(x^{2}-2 x-3\right)^{3}}\)

C. \(\frac{2\left(7 x^{3}+15 x^{2}+93 x-77\right)}{\left(x^{2}-2 x-3\right)^{3}} . \)

D. \( \frac{2\left(7 x^{3}-15 x^{2}-93 x+77\right)}{\left(x^{2}-2 x-3\right)^{3}}\)

A. \(A=0\)

B. \(A=2\)

C. \(\begin{aligned} &A=4 \cos x \end{aligned}\)

D. \(A=6 \sin x+4 \cos x\)

A. \(2 \sqrt{3}\)

B. \(-2 \sqrt{3}\)

C. 2

D. -2

A. -2

B. -4

C. \(2 \sqrt{3}\)

D. \(-2 \sqrt{3}\)

A. 54

B. -16

C. -18

D. 0

A. \(y=3 x^{2} .\)

B. \(y=2 x^{3} .\)

C. \(y=x^{3}\)

D. \(y=x^{2}\)

A. x = π/6 + kπ

B. x = π/4 + kπ

C. x = π/3 + kπ

D. x = kπ

A. \(14\sqrt 3\)

B. \(15\sqrt 3\)

C. \(16\sqrt 3\)

D. \(17\sqrt 3\)

A. -16

B. -15

C. -14

D. -13

A. 0

B. 1

C. 2

D. 3

A. \(- \dfrac{3}{2}\)

B. \(- \dfrac{5}{2}\)

C. \(- \dfrac{7}{2}\)

D. \(- \dfrac{9}{2}\)

A. 0

B. 1

C. 2

D. 3

A. -9

B. -8

C. -7

D. -6

A. 0; 4

B. 1; 4

C. 1; 2

D. 3; 1

A. -1

B. -2

C. 1/3

D. 9

A. \(\dfrac{-2}{{{{\left( {1 - x} \right)}^3}}}\)

B. \(\dfrac{2}{{{{\left( {1 - x} \right)}^5}}}\)

C. \(\dfrac{2}{{{{\left( {1 - x} \right)}^3}}}\)

D. \(\dfrac{2}{{{{\left( {1 - x} \right)}^2}}}\)

A. \(- \dfrac{1}{{x\sqrt x }}\)

B. \(- \dfrac{1}{{2x\sqrt x }}\)

C. \(- \dfrac{1}{{3x\sqrt x }}\)

D. \(- \dfrac{1}{{4x\sqrt x }}\)

A. y'' = -8sin4x - 2sin2x

B. y'' = 8sin4x + 2sin2x

C. y'' = -4sin4x - 2sin2x

D. y'' = -8sin4x + 2sin2x

A. \( \dfrac{2}{{9\sqrt[3]{{{x^5}}}}}\)

B. \( \dfrac{5}{{9\sqrt[3]{{{x^5}}}}}\)

C. \(- \dfrac{2}{{9\sqrt[3]{{{x^5}}}}}\)

D. \(- \dfrac{2}{{3\sqrt[3]{{{x^5}}}}}\)

A. \(\dfrac{{10}}{{{{\left( {x + 3} \right)}^3}}}\)

B. \(\dfrac{{ - 10}}{{{{\left( {x + 3} \right)}^3}}}\)

C. \(\dfrac{{5}}{{{{\left( {x + 3} \right)}^3}}}\)

D. \(\dfrac{{ - 5}}{{{{\left( {x + 3} \right)}^3}}}\)

A. \(\dfrac{1}{{4{x^2}\sqrt x }}\)

B. \(\dfrac{3}{{4{x^2}\sqrt x }}\)

C. \(\dfrac{5}{{4{x^2}\sqrt x }}\)

D. \(\dfrac{7}{{4{x^2}\sqrt x }}\)