Can't maple even maximize such a simple function?
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
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256
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