Question

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

• A. $3$
• B. $2$
• C. $1$
• D. $-1$

Answer 1

The correct option is A $3$

$y=3x^2+3\sin x$

$\Rightarrow \frac{dy}{dx}=6x+3\cos x$

Thus slope of tangent to the given curve at $x=0$ is

$=\frac{dy}{dx}{|}_{x=0}=(6x+3\cos x){|}_{x=0}=6\left(0\right)+3\cos 0=0+3\cdot 1=3$