Q. 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) (0, 0)
Explanation
(d)
Given curve is $y = x^{3}$
$\Rightarrow \ \ \ \ \ \ \frac{dy}{dx} = 3x^{2}$
Since, the tangent is parallel to $x$-axis
$\therefore\ \ \ \frac{dy}{dx} = 0\ \ \ \ \ \Rightarrow \ \ 3x^{2} = 0\ \ \ \ \Rightarrow \ \ \ \ x = 0,\ y = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.