Question

The abscissa of the point, where the tangent to curve

$y = x^{3} - 3x^{2} - 9x + 5$ is parallel to x-axis are

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

Answer 1

Answer: (D)

$x = - 1$ and 3

Answer 2

$y = x^{3} - 3x^{2} - 9x + 5$ ⇒ $\frac{dy}{dx} = 3x^{2} - 6x - 9$.

We know that this equation gives the slope of the tangent to the curve. The tangent is parallel to x-axis $\frac{dy}{dx} = 0$

Therefore, $3x^{2} - 6x - 9 = 0$ ⇒ $x = - 1,3$.