Question: maximize function, Weierstrass M-test

I would like to write a procedure which uses the Weierstrass M-test on uniform convergence. I wanted to use the maximize function (to recognize if the function is bounded and to get upper bound) but this function doesn't work in many simple cases. assume(x::float); assume(n::integer); maximize(2*sin(x)+cos(x));
          maximize(2 sin(x~) + cos(x~))
Actually, I don need maximize function but just to get any upper bound. Is there a way?
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