Question

Assertion (A): The points on the curve $y=x^3-3x$ at which the tangent is parallel to $x$-axis are $(1,-2)$ and $(-1,2).$
Reason (R): The tangent at $(x_1,y_1)$ on the curve $y=f\left(x\right)$ is vertical then $\frac{dy}{dx}$ at $(x_1,y_1)$ is not defined.

• A. Both A and R are true and R is the correct explanation for A
• B. Both A and R are true but R is not the correct explanation for A
• C. A is true but R is false
• D. A is false but R is true

Answer 1

Answer: (B)

Both A and R are true but R is not the correct explanation for A

$y^{\prime }=3x^2-3$
$y^{\prime }=0$
$\therefore$ tangent is parallel to x-axis
$x^2=1$
$x{=}_{-}^{+}1$
$y=-2$
$y=2$
y tangent is vertical then $\frac{dy}{dx}$ is not defined.