That's perfect! Thank you so much!
Hi Tom,
ClearAll@ξ ξ[a_, b_] := (a + b)/2 Manipulate[Plot[fxsquared[x], {x, a, b}, Epilog -> {Red, PointSize[0.02], Point[{ξ[a, b], fxsquared[ξ[a, b]]}]}, PlotRange -> {{0, 5}, {0, 25}}], {a, 1, 5}, {b, 1.01, 5}]
Do not set variables of constant values with :=, just use =
For the sake of Manipulate you do not need them at all. The following will give you the basic idea, and from there keep reading the documentation
Manipulate[Plot[Sin[x], {x, a, b}], {a, 0, 2 Pi}, {b, 3 Pi, 10 Pi}]
