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

---

Definitions:

Portfolio Performance

The assessment of how an investment portfolio has done in terms of returns for the risk taken, often compared against benchmarks or goals.

Treynor-Black Model

A special case of the Markowitz model of efficient diversification, derived by assuming returns are generated by the index model.

Residual Variance

The variance of the error terms in a regression model, representing the amount of variation that cannot be explained by the model's inputs.

Alpha/Beta

Measures in finance; Alpha represents the strategy's returns above the benchmark, whereas Beta indicates the volatility relative to the market.