Discuss the applicability of Rolle’s theorem for the following functions on the indicated intervals :

Question

Discuss the applicability of Rolle’s theorem for the following functions on the indicated intervals : f(x) = x 2/3 on [ – 1, 1]

Philoid · Accepted Answer

Given function is:

⇒ on [ – 1,1]

Let’s find the derivative of the given function:

⇒

Let’s check the differentiability of the function at x = 0.

⇒

Since the limit for the derivative is undefined at x = 0, we can say that f is not differentiable at x = 0.

∴ Rolle’s theorem is not applicable to the function ‘f’ on [ – 1,1].