Answer
Relative maximum: $x=1$
Relative minima: $x=2$ and $x=0$
Work Step by Step
First derivative
\[
f^{\prime}(x)=-12 x^{2}+8 x+4 x^{3}
\]
Critical points (zeros of first derivative or point where first derivative does not exist)
\[
x=2, x=1 \text { and } x=0
\]
Second derivative
\[
f^{\prime \prime}(x)=8-24 x+12 x^{2}
\]
Values of second derivative at critical points:
$f^{\prime \prime}(0)=8>0$
\[
f^{\prime \prime}(1)=-24+8-4+12<0
\]
$f^{\prime \prime}(2)=8>0$
\[
\begin{array}{l}
f^{\prime \prime}(1)=-24+8-4+12<0 \\
f^{\prime \prime}(2)=8>0
\end{array}
\]
Second derivative test
Relative minima: $x=2$ and $x=0$
Relative maximum: $x=1$