Henry Z.

asked • 10/28/21# Optimization question Ture or False

If f(x) is a differentiable function such that f'(7)=0, then f(x) either has a relative minimum at x=7 or a relative maximum at x=7

why the answer is false?

## 1 Expert Answer

Stanton D. answered • 10/28/21

Tutor to Pique Your Sciences Interest

Hi Henry Z.,

So draw f(x). Start at x=7; obviously the function graph is horizontal __right there, at that point__. But, that says nothing about what happens on either side! x=7 could be an inflection point, or maybe simply f(x) = c across the whole domain. Or various combinations, such as flat on one side for a while, then parabolic, etc., etc.

-- Cheers, --Mr. d.

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Joel L.

10/28/21