Question: Maximize does not seem to give the right solution



I am trying to maximize with respect to b, where

For s=0.19 trying (where obj(b) is the expression) I get that b=0 even though it is about 0.96 as the graph shows (and also the analytical solution )
Plotting the solution as a function of s, I get that the same happens for other values of s as well.

While in this example I do have a simple closed-form solution, for more complicated cases I want to be sure that Maximize() gives the correct answer!
Please, see the attached file for details

I use Maple 16.


Do you have any suggestion about why it is so and what to do about it?

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