Find the Derivative at Each Critical Point and Determine the Local

question 108

Multiple Choice

Find the derivative at each critical point and determine the local extreme values.
- $$y = \left\{ \begin{array} { l l } - \frac { 1 } { 4 } x ^ { 2 } - \frac { 1 } { 2 } x + \frac { 15 } { 4 } , & x \leq 1 \\x ^ { 3 } - 6 x ^ { 2 } + 8 x , & x > 1\end{array} \right.$$

• A)
• \(\begin{array}{l|l|l|l}
• \text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\
• \hline x=-1 & 0 & \text { local max } & 4 \\
• x=3.15 & 0 & \text { local min } & -3.08
• \end{array}\)
• B)
• \(\begin{array}{l|l|l|l}
• \text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\
• \hline x=-1 & \text { undefined } & \text { local min } & 4 \\
• x=3.15 & 0 & \text { local max } & -3.08
• \end{array}\)
• C)
• \(\begin{array}{l|l|l|l}
• \text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\
• \hline x=-1 & 0 & \text { local min } & 4 \\
• x=3.15 & 0 & \text { local max } & -3.08
• \end{array}\)
• D)
• \(\begin{array}{l|l|l|l}
• \text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\
• \hline x=1 & 0 & \text { local max } & 4 \\
• x=3.15 & \text { undefined } & \text { local max } & -3.08
• \end{array}\)

Understand the stages of sleep and their characteristics.

Recognize the physiological and psychological effects of substance use and withdrawal.

Comprehend the mechanisms and effects of hypnosis and dissociation theories.

Diagnose disorders based on symptoms related to visual processing and sleep patterns.

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