Find the Derivative at Each Critical Point and Determine the Local

question 127

Multiple Choice

Find the derivative at each critical point and determine the local extreme values.
- $$y = \left\{ \begin{array} { l l } 4 - x , & x < 0 \\4 + 3 x - x ^ { 2 } , & x \geq 0\end{array} \right.$$

• A)
• \(\begin{array}{l|l|l|l}
• \text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\
• \hline x=4 & \text { undefined } & \text { local min } & 4 \\
• x=0 & 0 & \text { local max } & \frac{25}{4}
• \end{array}\)
• B)
• \(\begin{array}{l|l|l|l}
• \text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\
• \hline x=0 & \text { undefined } & \text { local min } & 4 \\
• x=\frac{5}{2} & 0 & \text { local max } & \frac{41}{4}
• \end{array}\)
• C)
• \(\begin{array}{l|l|l|l}
• \text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\
• \hline x=0 & \text { undefined } & \text { local min } & -4 \\
• x=\frac{3}{2} & 0 & \text { local max } & \frac{7}{4}
• \end{array}\)
• D)
• \(\begin{array}{l|l|l|l}
• \text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\
• \hline x=0 & \text { undefined } & \text { local min } & 4 \\
• x=\frac{3}{2} & 0 & \text { local max } & \frac{25}{4}
• \end{array}\)

---

Definitions:

Paraprofessionals

Support professionals typically working alongside fully qualified professionals, often in educational or healthcare settings, providing supplementary assistance.

Providers of Color

Healthcare or service providers who identify as people of color, indicating diversity in the workforce.

Iatrogenesis

"Sickness or pathology that results from medical or psychological intervention and treatment."

Chinese American

An American citizen or resident of Chinese descent, often referring to a person's cultural identity integrating both Chinese and American elements.