Question

by inspecting the graph of the function, find the absolute maximum and absolute minimum on the given interval.

( p ( x ) = - sqrt 3 { x } + 1 ) on ( 27,64 )

find the absolute minimum. select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

a the absolute minimum is (-3) at (x = 64)
(use a comma to separate answers as needed.)
b. there is no absolute minimum

find the absolute maximum select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

a. the absolute maximum is at (x=)
(use a comma to separate answers as needed)
b. there is no absolute maximum

Explanation:

Step1: Evaluate the function at the endpoints

For \(x = 27\):
\(p(27)=-\sqrt[3]{27}+1\)
\(= - 3 + 1=-2\)
For \(x = 64\):
\(p(64)=-\sqrt[3]{64}+1\)
\(=-4 + 1=-3\)

Answer:

The absolute maximum is \(-2\) at \(x = 27\). The absolute minimum is \(-3\) at \(x = 64\).