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

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) (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 which is undefined at x = 0. Thus differentiability on (-1,1) is violated.
Note that the function is continuous on the interval [-1,1]. (since the squared cube-root function is continuous), and f(-1) = f(1) = 1.
RELATED QUESTIONS
Please help me verify Rolle's theorem for f(x)=(x-1)(x-2)(x-3) in the interval... (answered by Edwin McCravy)

supose that f(x) has derivative on the interval (a, b) is continuous on interval [a, b]... (answered by ikleyn)

Question is: Use the intermediate value theorem to show that the polynomial function... (answered by Fombitz)

PLEASE HELP ME WITH THIS PROBLEM: The table shows several value of the function... (answered by stanbon)

Consider the function f(x) = 1/2 (x + |x| ). Discuss continuity and smoothness for this... (answered by Boreal)

The table shows several value of the function f(x)= -x^3+x^2-x+2. Complete the missing... (answered by stanbon)

1)What does the Mean Value Theorem actually state about the function f(x)... (answered by solver91311)

Find the interval on which the function is increasing a) f(x) = |x+1| b) f(x) = x^3 (answered by robertb)

The table shows several value of the function f(x)=-x^3+x^2-x+2. Complete the missing... (answered by stanbon)