Question

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 $3$

Answer 1

The correct option is D $x=-1$ and $3$

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,
$\therefore \frac{dy}{dx}=0$
$\Rightarrow 3x^2-6x-9=0$
$\Rightarrow x=-1,3$