Question

If the tangent line at a point (x, y) on the curve y = f(x) is parallel to y-axis, find the value of $\frac{dx}{dy}$.

Answer 1

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