Find the derivative at each critical point and determine the local extreme values.
-$$y = \left\{ \begin{array} { l }
6 - 2 x , x \leq 1 \
x + 3 , x 1
\end{array} \right.$$
A)
$\begin{array}{l|l|l|l}
\text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \
\hline x=1 & \text { undefined } & \text { minimum } & 4
\end{array}$

B)
$\begin{array}{l|l|l|l}
\text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \
\hline x=2 & \text { undefined } & \text { minimum } & 5
\end{array}$

C)
$\begin{array}{l|l|l|l}
\text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \
\hline x=1 & 0 & \text { minimum } & 4
\end{array}$

D)
$\begin{array}{l|l|l|l}
\text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \
\hline x=0 & 0 & \text { minimum } & 5
\end{array}$

Question

Find the derivative at each critical point and determine the local extreme values.
-$$y = \left\{ \begin{array} { l } 
6 - 2 x , x \leq 1 \
x + 3 , x > 1
\end{array} \right.$$
A)
$\begin{array}{l|l|l|l}
\text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \
\hline x=1 & \text { undefined } & \text { minimum } & 4
\end{array}$

B)
$\begin{array}{l|l|l|l}
\text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \
\hline x=2 & \text { undefined } & \text { minimum } & 5
\end{array}$

C)
$\begin{array}{l|l|l|l}
\text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \
\hline x=1 & 0 & \text { minimum } & 4
\end{array}$

D)
$\begin{array}{l|l|l|l}
\text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \
\hline x=0 & 0 & \text { minimum } & 5
\end{array}$

Quizplus · Accepted Answer

The derivative of the piecewise function changes at $x = 1$, making it a critical point. The derivative is -2 for $x < 1$ and 1 for $x > 1$, but it is undefined exactly at $x = 1$ because the function changes form. At $x = 1$, the function value is 4, which is a minimum within the context of this piecewise function.

Find the Derivative at Each Critical Point and Determine the Local