Does a differentiable function have to have a relative minimum between any two relative maxima? Why?

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asked Aug 13, 2017 76.0k views

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Kelli · Answer 1 · 2017-08-18T12:13:21+0000

Yes, it does.

A differentiable function is continuous.

A relative maximum means that after the maximum the function starts to go down; then to reach a new maxium the function has to make a U-turn and start to go up. This U-turn point is a minimum

Does a differentiable function have to have a relative minimum between any two relative maxima? Why?

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