Question

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

Answer 1

The slope of the y-axis is $\infty$.
Also, the normal at (x, y) on the curve y = f(x) is parallel to the y-axis.
∴ Slope of the normal = Slope of the y-axis = $\infty$
$\text{⇒}\frac{dy}{dx}\text{=Slope of the tangent=}\frac{-1}{\text{Slope of the normal}}\text{=}\frac{-1}{\infty }\text{=0}$