Question

The abscissa(e) of the point(s), where the tangent to curve $y=x^{3}-3x^{2}-9x+5$ is parallel to the $x$ -axis is(are)

• A. $x=0$
• B. $x=1$ and $-1$
• C. $x=1$ and $-3$
• D. $x= \, -1 \, and \, 3$

Answer 1

Answer: (D)

$y=x^{3}-3x^{2}-9x+5$
$\Rightarrow $ $\frac{d y}{d x}=3x^{2}-6x-9$
We know that this equation gives the slope of the tangent to the curve. The tangent is parallel to $x$ -axis.
Therefore, $3x^{2}-6x-9=0$
$\Rightarrow \, $ $x=-1, \, 3$ .