Question:Can't maple even maximize such a simple function?

Question:Can't maple even maximize such a simple function?

Maple
Tried to maximize a simple function f(t), failed. Converted it to different forms, still failed. Simplified the function a bit by hand and tried again, still fail. Only after some major simplification by hand and a transformation: u=s^2=(1/2-t)^2, it finally worked. I must be missing something. I thought such a simple problem should certainly be solved by maple in a flash. Can someone enlighten me please? Thanks a lot. > maximize(t^2*(1-t)^2*(1+t^2)*(1+(1-t)^2), t = 0 .. 1); / 2 2 / 2\ / 2\ \ maximize\t (1 - t) \1 + t / \1 + (1 - t) /, t = 0 .. 1/ > maximize((1/2-s)^2*(1/2+s)^2*(1+(1/2-s)^2)*(1+(1/2+s)^2), s = (-1)/2 .. 1/2); / 2 2 / 2\ / 2\ \ |/1 \ /1 \ | /1 \ | | /1 \ | -1 1| maximize||- - s| |- + s| |1 + |- - s| | |1 + |- + s| |, s = -- .. -| \\2 / \2 / \ \2 / / \ \2 / / 2 2/ > maximize((1/4-s^2)^2*((5/4+s^2)^2-s^2), s = (-1)/2 .. 1/2); / 2 / 2 \ \ |/1 2\ |/5 2\ 2| -1 1| maximize||- - s | ||- + s | - s |, s = -- .. -| \\4 / \\4 / / 2 2/ > maximize((1/4-u)^2*((5/4+u)^2-u), u = 0 .. 1/4); 25 --- 256
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