Question

e figure below shows the derivative F' of a function F. If F(20) equals 100, estimate the maximum value attained by by F

Answer 1

Max occurs at x=50 where F'(x) = 0.

We need to find value for F(50) using fundamental theorem of calculus:
$\int\limits^{50}_{20} {F'(x)} \, dx = F(50) - F(20) = F(50) - 100$

$F(50) = 100+A$
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
$F(50) = 100+300 = 400$