Question: Maximization: change the output

Hello,
I have a question concerning the change of the results of Maximization procedure and it will be much appreciated if you could help me.
The case is: I need to find the maximum of a function (call if f(t)) given a range of values of another function (call it g(t)).Both sets of parameters are the same. I use "Maximize" command, but I need to plot the the results on (f,g) plane afterwards. How could I change the Maximization output in order to have only objective function values being observed and remembered? 
Hope, I've described the problem clearly, looking forward to find an answer with your help. Thenks in advance.  

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