Max occurs at x=50 where F'(x) = 0.
We need to find value for F(50) using fundamental theorem of calculus:
[tex] \int\limits^{50}_{20} {F'(x)} \, dx = F(50) - F(20) = F(50) - 100 [/tex]
[tex]F(50) = 100+A[/tex]
Where A is the estimated Area under the graph.
If we assume the shaded region is close to a right triangle then the Area is (1/2)*30*20 = 300
Therefore
[tex]F(50) = 100+300 = 400[/tex]
