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 = \[\infty\] \[\Rightarrow\frac{dy}{dx}=\text { Slope of the tangent }=\frac{- 1}{\text { Slope of the normal }}=\frac{- 1}{\infty}=0\]