# How do you verify that the hypothesis of the Mean Value Theorem are satisfied for #f(x)=sqrt(25-x^2)#?

##### 1 Answer

Sep 13, 2015

Refer to explanation

#### Explanation:

The hypothesis of the Mean Value Theorem requires that the function be continuous on some closed interval [a, b] and differentiable on the open interval (a, b).

The domain of the function is for all x reals that

Computing the derivative we get that

we see that is differentiable on the open

Hence MVT is satisfied.