Write the value
Question:

Write the value of $\frac{d y}{d x}$, if the normal to the curve $y=f(x)$ at $(x, y)$ is parallel to $y$-axis.

Solution:

Given that the normal to the curve $y=f(x)$ at $(x, y)$ is parallel to $y$-axis.

We know that the slope of the $y$-axis is $\infty$.

$\because$ Slope of the normal = Slope of the $y$-axis $=\infty$

$\therefore$ Slope of the tangent $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{-1}{\text { Slope of the normal }}=\frac{1}{\infty}=0$