Thread: Antiderivatives with graphs

Using the graph of g' shown below and the fact that g(0) = 100, sketch a graph of g(x). Find the coordinates of all the critical points and inflection points of g.

(a) The critical points of g occur at what points?

(b) The inflection points of g occur at what points?





The two critical points are x=15 and x=40 and the two inflection points are x=10 and x=20. I really am at a loss of what I can do in this problem, but it seems this should be pretty easy.

Use the areas under/over the graph. E.g. how does this first, red one (easy enough to calculate) help you find g(10)?