Question

Determine the location and values of the absolute maximum and absolute 

minimum for the given function: 

𝑓(𝑥) = (−𝑥 + 2)⁴, 𝑤ℎ𝑒𝑟𝑒 0 ≤ 𝑥 ≤ 3

Answer 1

f(x)=(-x+2)⁴ , 0 ≤ 𝑥 ≤ 3

d/dx= 4(-x+2)³

d/dx=0

4(-x+2)³=0

-x+2=0; x=2

f(0)=(0+2)⁴=(2)⁴=16

the absolute minimum point is therefore at x=2 where the value is 0.

the absolute maximum point is at x=0 where the value is 16