Question

find the absolute extrema of the function on the closed interval.
$f(x)=8 - x$, $-2,4$
minimum $(x,y)=(quad)$
maximum $(x,y)=(quad)$

Explanation:

Step1: Find the derivative of the function

The derivative of \(f(x)=8 - x\) is \(f^\prime(x)=-1\). Since \(f^\prime(x)\) is never zero (it is a constant non - zero value), there are no critical points in the open interval \((-2,4)\).

Step2: Evaluate the function at the endpoints of the interval

• When \(x=-2\):

\(y = f(-2)=8-(-2)=8 + 2=10\)

• When \(x = 4\):

\(y=f(4)=8-4=4\)

Answer:

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