When I try to illustrate a region by filling it, Mathematica (v11) seems to miss a the corner.
Here are my commands.
f1[x_] := x/2 + 5
f2[x_] := 5 - x^2
f3[x_] := 4 x
x1 = x /. Solve[f2[x] == f3[x], x][[2]]
x2 = x /. Solve[f1[x] == f3[x], x][[1]]
Show[
RegionPlot[
f2[x] <= y <= f1[x] && 0 <= x <= x1 ||
f3[x] <= y <= f1[x] && x1 <= x <= x2 ,
{x, 0, x1 + 0.5}, {y, 0, f1[x1 + 1]}
],
Plot[{f1[x], f2[x], f3[x]}, {x, 0, 2}]
]
This is what it looks like:
PlotPointsoption ofRegionPlot. Alternatively, you might want to fill the area like here. – Lukas Lang May 20 '18 at 15:57