# How do you determine all values of c that satisfy the conclusion of the mean value theorem on the interval [0, 8] for #f(x) = x^3 + x - 1#?

##### 2 Answers

Solve the equation

#### Explanation:

The only value of

x=

#### Explanation:

The mean value theorem states:

so you have

Plug 8 and 0 into the equation

f(8)= 512 + 8 - 1 = 519

f(0)= 0 + 0 - 1 = -1

Now take the derivative of the function

x=

x=