by **HallsofIvy** » Wed Sep 09, 2020 12:12 pm

Didn't I see this on a different web-site some last week? Didn't you like those answers?

A "critical point" of a graph occurs where the tangent line to the graph is horizontal or the derivative does not exist. Looking at this graph, it looks like the tangent line is horizontal at x= 4.5 and x= 13. (What happens for x negative is not clear.) The function itself is not defined at x= 10 so there is no derivative there.

Do you understand what "increasing" and "decreasing" mean? Isn't it clear that the function is increasing from x= -1 to 4.5 and from x= 10 to 13. Where is it decreasing?

Just "eye-balling" the the graph I would say the maximum at x= 4.5 is slightly higher than the maximum at x= 13 so the "absolute maximum" is at x= 4.5.