# Using the principle of the mean-value theorem on the indicated interval, how do you find all numbers c that satisfy the conclusion of the theorem for #f(x) = 5(1 + 2x)^(1/2)# in the interval [1,4]?

##### 1 Answer

Oct 19, 2015

Solve the equation that is the conclusion to the Mean Value Theorem. Choose only the solutions in the interval

#### Explanation:

Find

The algebra is tedious.

So we need to solve:

So, we need

So

Note that, since