Question

The slopes of the normal to the curve $y=2x^2+3\sin x$ at $x=0$ is

• A. $\frac{1}{3}$
• B. $3$
• C. $-\frac{1}{3}$
• D. $-3$

Answer 1

The correct option is C $-\frac{1}{3}$

Given : $y=2x^2+3\sin x$
Slope of tangent is $\frac{dy}{dx}:$
Differentiating w.r.t. $x,$
$\frac{dy}{dx}=4x+3\cos x$
$\text{Slope of tangent}\times \text{Slope of Normal}=-1$
Slope of Normal $=\frac{-1}{4x+3\cos x}$
Putting $x=0$
Slope of Normal $=\frac{-1}{4\left(0\right)+3\cos 0}=-\frac{1}{3}$
Hence, correct answer is $\left(D\right)$.