SOLUTION: The question is : Discuss applicability of Roll's Theorem for the function f(x) = (x)^(2/3) on the interval [-1,1] Please send step by stem solution, Regards, S B Roy

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Question 890063: The question is : Discuss applicability of Roll's Theorem for the function
f(x) = (x)^(2/3) on the interval [-1,1]
Please send step by stem solution,
Regards,
S B Roy
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Rolle's theorem CANNOT be applied on the interval [-1,1], because the function is not differentiable at x = 0. The derivative function is df%28x%29%2Fdx+=+2%2F%283x%5E%281%2F3%29%29 which is undefined at x = 0. Thus differentiability on (-1,1) is violated.
Note that the function f%28x%29+=+x%5E%282%2F3%29 is continuous on the interval [-1,1]. (since the squared cube-root function is continuous), and f(-1) = f(1) = 1.