$(1$ point$)$ Use an appropriate theorem to complete the following statement.

If $f$ is differentiable and $c{f}^{\text{'}}(c)f(1),$ then there $is$ a number $c,in$ the interval $()$ such that $f^{\text{'}}(c)$

What theorem guarantees this?

The Mean Value Theorem

$(Be$ sure that you can carefully apply this theorem $to$ obtain the indicated result!$)$