If $y=2 x(x-1)(2-x)$; then $\frac{d^2 y}

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Determinants

Question:

If $y=2 x(x-1)(2-x)$; then $\frac{d^2 y}{dx^2}$ is :

Options:

$6-12 x$

$12(1+x)$

$12(1-x)$

$6+2 x$

Correct Answer:

$12(1-x)$

Explanation:

$y=2 x(x-1)(2-x)$

$y=2 x\left(2 x-x^2-2+x\right)$

$y=2 x\left(-x^2+3 x-2\right)$

$y=-2 x^3+6 x^2-4 x$

so differentiating y w.r.t x

$\frac{d y}{d x}=-6 x^2+12 x-4$

differentiating again wrt (x)

$\frac{d^2 y}{d x^2}=-12 x+12$

$=+12(1-x)$