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.(2 points)

Answer 1

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 limited by the maximum number of times the polynomial's derivative can change signs, which is one less than the degree of the polynomial (in this case, \(5 - 1 = 4\)).