Find the Derivative at Each Critical Point and Determine the Local

question 143

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

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