Answer
See explanation.
Work Step by Step
Points where the tangent line is horizontal (and thus derivative is zero) are critical points, meaning the function is not differentiable.
\[
x=\sqrt[3]{5} \text { and } x=0
\]
Using the first derivative test
$x=0$ is a double root, so $x=0$ is not a relative extremum.
Use first derivative test
$f^{\prime}(x)<0$ on the left and $f^{\prime}(x)>0$ on the right of $x=\sqrt[3]{5},$ so $\sqrt[3]{5}=x$ is a relative minimum.