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Homework Statement
The specific problem can be found here: http://www.cbsd.org/sites/teachers/hs/cmcglone/Student%20Documents/Chapter%204%20(Application%20of%20Derivatives)/Section%204.3%20-%20Olsen%20Curve%20Sketching%20Answers.pdf"
The above link also gives the answer. I am not sure on how to get there.
So, my question is: How does one find the maximum value of a function, on a closed interval, given only the graph of the first derivative?
Homework Equations
Because the question is solely graphical, no equations are needed. However, knowledge of the following theorems are:
Extreme Value Theorem
Rolle's Theorem
Mean Value Theorem
and
The First Derivative Test
The Attempt at a Solution
Well, if I had the equation to f(x), then I could simply plug the critical points into f(x) and the highest value would be the answer.
Perhaps it has something to do with the slope around the point? Or perhaps the answer can be found using a theorem I am not aware of?
OH, -5 is an endpoint! Surely, this must be critical information! But still, how does one determine for sure that this is the maximum value? I know it is a possible candidate.
And that's as far as I get.
Thanks for the help, in advance
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