Find the Derivative at Each Critical Point and Determine the Local

question 107

Multiple Choice

Find the derivative at each critical point and determine the local extreme values.
- $$y = x ^ { 2 } \sqrt { 1 - x }$$

• A)
• \(\begin{array}{l|l|l|l}
• \text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\
• \hline x=\frac{4}{5} & 0 & \text { local max } & \frac{16}{125} \sqrt{5}
• \end{array}\)
• B)
• \(\begin{array}{l|l|l|l}
• \text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\
• \hline x=0 & 0 & \text { min } & 0 \\
• x=1 & 0 & \text { min } & 0 \\
• x=\frac{4}{5} & 0 & \text { local } \max & \frac{16}{125} \sqrt{5}
• \end{array}\)
• C)
• \(\begin{array}{l|l|l|l}
• \text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\
• \hline x=0 & 0 & \min & 0 \\
• x=1 & \text { undefined } & \text { min } & 0 \\
• x=\frac{4}{5} & 0 & \text { local max } & \frac{16}{125} \sqrt{5}
• \end{array}\)
• D)
• \(\begin{array}{l|l|l|l}
• \text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\
• \hline x=1 & \text { undefined } & \text { min } & 0 \\
• x=\frac{4}{5} & 0 & \text { local } \max & \frac{16}{125} \sqrt{5}
• \end{array}\)

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