Find the Derivative at Each Critical Point and Determine the Local

Multiple Choice

Find the derivative at each critical point and determine the local extreme values.
- $$y = x ^ { 2 / 3 } \left( x ^ { 2 } - 16 \right) ; x \geq 0$$

A)
$\begin{array}{l|l|l|l}\text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\\hline x=0 & \text { Undefined } & \text { local max } & 4 \\x=2 & 0 & \text { minimum } & -19.049\end{array}$

B)
$\begin{array}{l|l|l|l}\text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\\hline x=0 & \text { Undefined } & \text { local max } & 0 \\x=2 & 0 & \text { minimum } & 31.748\end{array}$

C)
$\begin{array}{l|l|l|c}\text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\\hline x=0 & \text { Undefined } & \text { local max } & 0 \\x=2 & 0 & \text { minimum } & -19.049\end{array}$

D)
$\begin{array}{l|l|l|l}\text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\\hline x=0 & 0 & \text { maximum } & 0 \\x=2 & 0 & \text { minimum } & -19.049\end{array}$