Answer
Stationary: $x=0$
Critical: $x=\pm 5$ and $x=0$
Work Step by Step
First derivative
\[
\frac{2 x}{3}\left(-25+x^{2}\right)^{-2 / 3}=f^{\prime}(x)
\]
Points where the derivative is zero are stationary points.
\[
\frac{2 x}{3}\left(-25+x^{2}\right)^{-2 / 3}=0
\]
A fraction is zero if the numerator is zero
\[
2 x=0
\]
Points where the tangent line is horizontal (thus, the derivative is zero) are critical points, since the function is not differentiable.
\[
x=0
\]
Roots
\[
x=0 \text { and } x=\pm 5
\]
Points where the first derivative is zero are stationary points.
\[
x=0
\]
