Question

f(x) = −x^2 + 3x
on [0,3]. What is its maximum value?

Answer 1

f ' (x) = -2x + 3
solve f '(x) = 0
-2x + 3 = 0 , x = 3/2

compare:
f(0) = 0
f(3/2)= 2.25
f(3) = 0

so the absolute max is 2.25

Answer 2

on the domain *