Question

What is the absolute extrema of f(x)=sin^2(2x). Intervals [0,pi]

Answer 1

clearly, since 0 <= |sin x| <= 1, the extrema are where sin^2(2x) = 1 or 0

That is, sin(2x) = ±1 or sin(2x) = 0
In the indicated domain, that leaves
2x = π/2 or 3π/2 or 0 or π or 2π
x = π/4 or 3π/4 or 0 or π/2 or π

See the graph at

http://www.wolframalpha.com/input/?i=sin^2%282x%29