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

##### 1 Answer

The Mean Value Theorem has two hypotheses:

**H1** :

**H2** :

In this question,

This function is a polynomial, so it is continuous on its domain,

So

**So, both hypotheses are satisfied.**

Because the hypotheses are satisfied, we can be sure that there is a

To find the

#f'(x) = (f(1)-f(-1))/(1-(-1))# .

If there are solutions outside the interval

In this case the only solution is