Show that f(x) = X^{1/3} is not differentiable at x = 0.

Question

Show that f(x) = \(X^\frac{1}{3}\) is not differentiable at x = 0.

Answer 1

For differentiability,

LHD(at x = 0) = RHD (at x = 0)

= Not defined

= Not defined

Since, LHD and RHD does not exist at x = 0

Hence, f(x) is not differentiable at x = 0