Find the Derivative at Each Critical Point and Determine the Local

question 135

Multiple Choice

Find the derivative at each critical point and determine the local extreme values.
- $y=x^{2} \sqrt{9-x}$

• A)
• \(\begin{array}{l|l|l|l}
• \text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\
• \hline x=0 & 0 & \text { min } & 0 \\
• x=9 & \text { undefined } & \text { min } & 0 \\
• x=\frac{36}{5} & 0 & \text { local max } & \frac{3888}{125} \sqrt{5}
• \end{array}\)
• B)
• \(\begin{array}{l|l|l|l}
• \text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\
• \hline x=9 & \text { undefined } & \text { min } & 0 \\
• x=\frac{36}{5} & 0 & \text { local max } & \frac{3888}{125} \sqrt{5}
• \end{array}\)
• C)
• \(\begin{array}{l|l|l|l}
• \text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\
• \hline x=0 & 0 & \min & 0 \\
• x=9 & 0 & \min & 0 \\
• x=\frac{36}{5} & 0 & \text { local max } & \frac{3888}{125} \sqrt{5}
• \end{array}\)
• D)
• \(\begin{array}{l|l|l|l}
• \text { Critical Pt.| } & \text { derivative } & \text { Extremum } & \text { Value } \\
• \hline \mathrm{x}=\frac{36}{5} & 0 & \text { local max } & \frac{3888}{125} \sqrt{5}
• \end{array}\)