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.
Francisco’s answer is incorrect because a polynomial of degree five can have a maximum of four relative extrema, not five. The number of relative extrema is always one less than the degree of the polynomial.
Francisco's answer is incorrect because a polynomial of degree five can have up to four relative extrema, but it is not limited to only five. The number of relative extrema that a polynomial can have depends on the behavior and shape of the polynomial graph.
