# Given the function #f(x) = x^(2/3)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-1,8] and find the c?

##### 1 Answer

The Mean Value Theorem has two hypotheses:

**H1** :

**H2** :

In this question,

This function is continuous on its domain,

So **not ** differentiable on

To determine whether there is a

#f'(c) = (f(8)-f(-1))/(8-(-1)) = (4-1)/9 = 1/3#

We can actually solve

We get

For an example of a function on an interval where it does not satisfy the hypotheses, but does satisfy the conclusion, please see:

https://socratic.org/questions/given-the-function-f-x-x-1-3-how-do-you-determine-whether-f-satisfies-the-hypoth