Question

Find points at which the tangent to the curve $y=x^3-3x^2-9x+7$ is parallel to the $x$-axis

• A. $(3,-20)$ and $(-1,12)$
• B. $(3,20)$ and $(1,12)$
• C. $(3,-10)$ and $(1,12)$
• D. $(3,10)$ and $(1,-12)$

Answer 1

Answer: (A)

$(3,-20)$ and $(-1,12)$

Given, $y=x^3-3x^2-9x+7$

Slope $=\frac{dy}{dx}=3x^2-6x-9$
If tangent is parallel to the $x$-axis, then $\frac{dy}{dx}=0$
$\Rightarrow 3x^2-6x-9=0$

$\Rightarrow x^2-2x-3=0$
$\Rightarrow x^2-3x+x-3=0$

$\Rightarrow (x-3)(x+1)=0$
$\Rightarrow x=3$ or $x=-1$

$\Rightarrow y=-20$ and $y=12$