Find the Derivative at Each Critical Point and Determine the Local

question 138

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

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