<< Optimization`UnconstrainedProblems`
findMaximumPlot // ClearAll;
findMaximumPlot[{f_, cons_}, rest__] :=
Internal`InheritedBlock[{FindMinimum},
Unprotect@FindMinimum;
FindMinimum[obj_, r___] /; ! TrueQ[$in] := Block[{$in = True},
FindMaximum[{f, cons}, r]
];
Protect@FindMinimum;
FindMinimumPlot[f, rest]
];
problem = {-0.248226 Cos[2 x] - 0.0184829 Cos[4 x] -
0.0594608 Cos[x] Sin[x] + 0.123626 Sin[4 x], 0 <= x <= 3/2};
findMaximumPlot[problem, {{x, 3/4}},
PlotStyle -> Directive[Opacity[0.5], Red]]