Thank you. Good lecture. I wonder about your graph of F. I suppose in (2,3) interval graph should be concave up and from 3 to 5 (3,5) interval the graph of F should be concave down according to the information of derivative. Am I correct?
Yes, Pranav is correct: this video is incorrect and one of the errors is the concavity on (2,3). Another error is the concavity on (3,5) (it should also be concave down). Other errors are that F must be differentiable (so "smooth and curvy" not "sharp and pointy") at both 2 and 3 since f=F' exists at those values but the graph drawn in the video is nondifferentiable at 2 and 3. More specifically, since f(3)=0, the slope of F should be 0 at 3.
