Question

Given the function `f(x)=1/sqrt(x+2)`, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-1,23] and find the c?

Answer 1

Is `f` continuous on `[-1,23]`?
Is `f` differentiable on `(-1,23)`?

If the answer to both is "yes", the `f` satisfies the hypotheses on the interval.

The conclusion of the MVT is

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

To find the `c`, solve the equation. Discard any solutions outside the interval.