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

---

Definitions:

Slowly

With low speed; not quickly or rapidly.

Uncertainty

The state of being unsure or having doubts.

Nonverbal Sensitivity

The ability to accurately encode (express) and decode (understand) nonverbal cues.

Social Competence

The ability to handle social interactions and relationships effectively, including communication and understanding social cues.