I'm trying to define the region between two curves, f[x]
and g[x]
, I can easily find where they intersect:
f = Function[x, 12 x^2];
g = Function[x, 3 x^3];
p = {x, g[x]} /. DeleteDuplicates[Solve[g[x] == f[x], x, Reals]];
p1 = First[Take[p, 1]];
p2 = First[Drop[p, 1]];
From there I plot the curves:
plot = Plot[Evaluate@Through[{f, g}@x], {x, 0, 4},
PlotRange -> {{0, 4}, {0, 200}},
Epilog -> {Red, PointSize[0.02], Point@{p1, p2}},
PlotLabels -> Automatic]
And all of that works fine, my problem is when I try and define the intersection of those two regions
rf = ImplicitRegion[y <= f[x], {x, y}];
rg = ImplicitRegion[y >= g[x], {x, y}];
intersection = RegionIntersection @@ {rf, rg};
Region[rf, PlotRange -> {{0, 4}, {0, 200}}]