Question

find the absolute extrema of the function on the closed interval.

$f(x)=8 - x, \quad -2,4$

minimum $(x,y)=\left(\

$$\begin{array}{l}\\square\\end{array}$$

\
ight)$

maximum $(x,y)=\left(\

$$\begin{array}{l}\\square\\end{array}$$

\
ight)$

Explanation:

Step1: Find the derivative

The derivative of \(f(x)=8 - x\) is \(f^\prime(x)=-1\). Since \(f^\prime(x)\) is a constant (\(- 1
eq0\)), there are no critical points in the open interval \((-2,4)\).

Step2: Evaluate the function at the endpoints

• For \(x=-2\): \(y = f(-2)=8-(-2)=10\)
• For \(x = 4\): \(y=f(4)=8 - 4=4\)

Answer:

minimum \((x,y)=(4,4)\)
maximum \((x,y)=(-2,10)\)