Find the Derivative at Each Critical Point and Determine the Local

question 316

Multiple Choice

Find the derivative at each critical point and determine the local extreme values.
- $y = \left\{ \begin{array} { l } 7 - 2 x , x \leq 1 \\x + 4 , x > 1\end{array} \right.$

• A)
• \(\begin{array}{l|l|l|l}
• \text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\
• \hline x=1 & \text { undefined } & \text { minimum } & 5
• \end{array}\)
• B)
• \(\begin{array}{l|l|l|l}
• \text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\
• \hline x=0 & 0 & \text { minimum } & 6
• \end{array}\)
• C)
• \(\begin{array}{l|l|l|l}
• \text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\
• \hline x=2 & \text { undefined } & \text { minimum } & 6
• \end{array}\)
• D)
• \(\begin{array}{l|l|l|l}
• \text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\
• \hline x=1 & 0 & \text { minimum } & 5
• \end{array}\)

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Definitions:

Synapse

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Central Nervous System

The section of the nervous system consisting of the brain and spinal cord, tasked with interpreting and dispatching nerve signals.

Spinal Cord

A long, thin, tubular structure made up of nervous tissue, extending from the brainstem down the back, conducting signals to and from the brain.

Parasympathetic Division

A division of the autonomic nervous system that is involved in rest-and-digest functions, conserving energy and restoring the body to a state of calm.