rolle's theorem
f must be continuous on a closed interval [a,b]
differential on (a,b) with f(a)=f(b)
Then, there is atleast one point C in (a,b) such that f'(c)=0
I am suppose to determine if rolle's theorem applies to the fuction and solve
in the inverval [-1,1]
Mathab says the assumptions for the Theorem have not been satisfied. I am under the impression they are satisfied. I was wonderifing if someone could provide and explanation as to why the theorem has not been satisfied.
It certainly is...
f(-1) = 1 - (-1)^(2/3) = 1 - [(-1)^2]^(1/3) = 1 - 1^(1/3) = 1 - 1 = 0
and
f(1) = 1 - 1^(2/3) = 1 - [1^2]^(1/3) = 1 - 1^(1/3) = 1 - 1 = 0.
However, Deveno is right about the function not being differentiable in this entire region. So I was wrong about Rolle's Theorem being satisfied