Determine the location and values of the absolute maximum and absolute minimum for the given function

Question

f(x)=(-x+2)^4,

Answer 1

there is no absolute maximum f(x) approaches infinity, as x approaches + or - infinity.

infinity is the limit of f(x) but it's not a real number, "just" a limit. But if you include surreal numbers, the maximum is infinity. Infinity is a "surreal" number. Not real, "just" surreal.

absolute minimum exists. It's the point (2,0) or f(x) =0 take the derivative and set = 0

f(x) = (2-x)^4

f'(x) = 4(2-x)^3(-1) = 0

-4(2-x)^3 = 0

(2-x)^3 = 0

x =2, y=0