Determine the relative maximum and minimum on the graph

Determine the relative maximum and minimum on the graph

Postby jaychay » Sun Sep 06, 2020 1:36 pm

Given that f is the function on (−∞, ∞) and the graph is the derivative of f

1.) Find the critical point on the graph ?
2.) Find the interval of the increasing function on the graph ?
3.) Find the interval of the decreasing function on the graph ?
4.) Find the point which is the absolute maximum on the graph ?
5.) Find the point which is the absolute minimum on the graph ?
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Re: Determine the relative maximum and minimum on the graph

Postby 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.

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