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