The first step is come up with a simple example of your question. This will make it easier to show how this is done.
Here's a simplified version of your problem:
exampleFunctions = Table[a Sin[a x], {a, 0, 1, 0.1}];
Plot[exampleFunctions, {x, 0, 10}, PlotRange -> All]
How can we run FindMaximum on every function in eampleFunctions? Using Map:
getMaxValue[function_] := FindMaximum[function, {x, 0}]
maxvals = Map[getMaxValue, exampleFunctions]
Note that this doesnt' 100% work for this example. We would have to tweak how we find the max values. Still we can plot these max values:
dataToPoints[{yval_, {x -> xval_}}] := {xval, yval}
maxPoints = Map[dataToPoints, maxvals]
ListPlot[maxPoints]
And naively join the plots together:
Show[Plot[exampleFunctions, {x, 0, 10}, PlotRange -> All], ListPlot@maxPoints]