Question

The slope of the normal to the curve y = 2x2 + 3 sin x at x = 0 is

Answer 1

The equation of the given curve is.

The slope of the tangent to the given curve at x = 0 is given by,

$\frac{dy}{dx}$]x=0=4x+3cosx]x-0=0+3cos0=3

Hence, the slope of the normal to the given curve at x = 0 is

$\frac{-1}{slope\,of\,the\,tangent\,at\,x=0}$=$-\frac{1}{2}$.

The correct answer is D.