#### Answer

$ c= ±\sqrt {7}$

#### Work Step by Step

The slope of the secant line is
$\frac{f(b)-f(a)}{b-a}=\frac{f(5)-f(-4)}{5-(-4)}=\frac{5^{3}-(-4)^{3}}{9}=21$
We must find $ c $ such that $ f'(c)=21$.
$ f'(c)=3c^{2}=21\implies c^{2}=\frac{21}{3}=7$
$\implies c= ±\sqrt {7}$
The value $ c=±\sqrt {7}$ lies in (-4, 5) and satisfies $ f'(±\sqrt {7})=21$. This satisfies the conclusion of the MVT.