Discuss the applicability of Rolle’s theorem for the following functions on the indicated intervals :
f(x) = x2/3 on [ – 1, 1]
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].