If $y=2 x(x-1)(2-x)$; then $\frac{d^2 y}{dx^2}$ is :
Answer & explanation
Correct answer: option 3
$y=2 x(x-1)(2-x)$
$y=2 x\left(2 x-x^2-2+x\right)$
$y=2 x\left(-x^2+3 x-2\right)$
$y=-2 x^3+6 x^2-4 x$
so differentiating y w.r.t x
$\frac{d y}{d x}=-6 x^2+12 x-4$
differentiating again wrt (x)
$\frac{d^2 y}{d x^2}=-12 x+12$
$=+12(1-x)$