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.
- $y = \left\{ \begin{array} { l l } 8 - x , & x < 0 \\ 8 + 7 x - x ^ { 2 } , & x \geq 0 \end{array} \right.$

A)
$\begin{array}{l|l|l|l}\text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\\hline x=0 & \text { undefined } & \text { local min } & 8 \\x=\frac{7}{2} & 0 & \text { local max } & \frac{81}{4}\end{array}$

B)
$\begin{array}{l|l|l|l}\text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\\hline x=8 & \text { undefined } & \text { local min } & 8 \\x=0 & 0 & \text { local max } & \frac{81}{4}\end{array}$

C)
$\begin{array}{l|l|l|l}\text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\\hline x=0 & \text { undefined } & \text { local min } & 8 \\x=\frac{9}{2} & 0 & \text { local max } & \frac{113}{4}\end{array}$

D)
$\begin{array}{l|l|l|l}\text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\\hline x=0 & \text { undefined } & \text { local min } & -8 \\x=\frac{7}{2} & 0 & \text { local max } & -\frac{17}{4}\end{array}$