Question

How do you determine all values of c that satisfy the conclusion of the mean value theorem on the interval [-1, 23] for `f(x)=1/sqrt(x+2)`?

Answer 1

See below.

Explanation:

The conclusion of the MVT says

there is a `c` in `(-1,23)` such that `f'(c) = (f(23)-f(-1))/(23-(-1))`.

To find the `c`, solve the equation on the interval `(-1,23)`.

You should get `c = -2+ 15^(2/3)`.