What is the maximum number of relative extrema contained in the graph of this function?

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asked Mar 28, 2019 225k views

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Kerol · Answer 1 · 2019-04-03T08:29:28+0000

Answer: The maximum number of relative (local) extrema is 3.

Explanation: the polynomial is of 4th degree. Its derivative is a polynomial of a 3rd degree, which may have up to 3 roots (tied to extrema of the original polynomial). If all 3 roots are real each with multiplicity of 1, then the original polynomial will show 3 relative extrema.

What is the maximum number of relative extrema contained in the graph of this function?

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