Question: How to plot the extremums of a function?

I tried to get the maximum points of a function of 3 independent variables (f(a,b,t)) in time domain. and plot the maximum points as function of a and b. f(1.3,1.3,t) is as below:


but "maple" is not able to calculate the maximum of this function analytically and must try out optimization box. Please advise me how to plot the function "g(a,b):=Maximize(f(a,b,t),t=0..Pi)" where the analytical solution is not obtainable.


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