Question

The points on the graph $y=x^3-3x$ at which the tangent is parallel to $x$-axis are :

• A. $(2,2)$ and $(1,-2)$
• B. $(-1,2)$ and $(-2,-2)$
• C. $(2,2)$ and $(-1,2)$
• D. $(-2,-2)$ and $(2,2)$
• E. $(1,-2)$ and $(-1,2)$

Answer 1

The correct option is E $(1,-2)$ and $(-1,2)$

Given, curve is $y=x^3-3x$ .....(i)
On differentiating w.r.t. $x$, we get
$\frac{dy}{dx}=3x^2-3$
Since, tangent is parallel to $x$-axis.
Therefore, $\frac{dy}{dx}=0$
$\Rightarrow 3x^2-3=0$

$\Rightarrow x^2=1$
$\Rightarrow x=\pm 1$
From equation (i), we have
When $x=1,y=1^3-3\left(1\right)=-2$
When $4x_1=-1,y=(-1{)}^3-3(-1)=2$
Therefore, required points are $(1,-2)$ and $(-1,2)$.