Answer
See explanation.
Work Step by Step
(a) $g^{\prime}(x)=-24 x^{2}+12 x^{3}$, $f^{\prime}(x)=5 x^{4}$
So $g^{\prime}(0)=0$ and $f^{\prime}(0)=0$
Points where the first derivative is zero are stationary points.
(b) Nothing can be concluded because the second derivatives of $f$ and $g$ are also zero at the stationary point $0=x$
Apply first derivative test.
(c) $f^{\prime}(x)>0$ if $x<0$ and $f^{\prime}(x)>0$ if $x>0,$ so $1=x$ isn't a relative extremum.
$g^{\prime}(x)<0$ if $x<0$ and $g^{\prime}(x)<0$ if $x>0,$ so $0=x$ isn't a relative extremum.
