Q. The abscissa of the points, where the tangent to 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)
Given, $y = x^{3} - 3x^{2} - 9x + 5$
$\Rightarrow \ \ \frac{dy}{dx} = 3x^{2} - 6x - 9$
We know that, this equation gives the slope of the tangent to the curve. The tangent is parallel to $x$-axis.
$\therefore\ \ \frac{dy}{dx} = 0\ \ \ \ \ \Rightarrow \ \ \ \ 3x^{2} - 6x - 9 = 0$
$\Rightarrow \ \ \ \ \ \ x = - 1,\ 3$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.