Q. The abscissa of the points, where the tangent to the curve $y = x^{3} - 3x^{2} - 9x + 5$ is parallel to $x$-axis, are
A) $x = 0$ and 0
B) $x = 1$ and $- 1$
C) $x = 1$ and $- 3$
D) $x = - 1$ and 3
Explanation
(d)
$\because\ \ y = x^{3} - 3x^{2} - 9x + 5$
On differentiating w.r.t. $x$, we get
$\frac{dy}{dx} = 3x^{2} - 6x - 9$
Since, tangent is parallel to $x$-axis
$\therefore\ \ \frac{dy}{dx} = 0\ \ \ \Rightarrow \ \ \ 3x^{2} - 6x - 9 = 0$
$\Rightarrow \ \ \ (x + 1)(x - 3) = 0\ \ \ \Rightarrow \ \ \ \ x = - 1,\ 3$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.