Question

The point on the curve $y=x^3$ at which the tangent to the curve is parallel to the $x$ axis is

• A. $(2,2)$
• B. $(3,3)$
• C. $(4,4)$
• D. $\left(0,0\right)$

Answer 1

The correct option is D

$\left(0,0\right)$

Compute the required point:

Given: $y=x^3$………………$\left(1\right)$

Differentiate with respect to $x$,

$\frac{dy}{dx}=3x^2$

Since the tangent to the curve is parallel to the $x$axis,

Therefore, $\frac{dy}{dx}=0$

$\Rightarrow$ $3x^2=0$

$\Rightarrow$ $x=0$

Substitute the value of $x$ in equation $\left(1\right)$,

$y=0$

Hence the point is $\left(0,0\right)$.

Option $\left(D\right)$ is the correct option.