Francisco's answer is incorrect because a polynomial of degree five can have at most four relative extrema, not five. This is due to the fact that the number of relative extrema is at most one less than the degree of the polynomial, as relative extrema occur at the critical points where the first derivative changes sign.
Francisco's teacher asked him to describe the number of relative extrema a polynomial of degree five could have. Francisco answered, "The polynomial will have exactly five relative extrema." Write 1-2 sentences discussing why Francisco's answer is incorrect.
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