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 2 sentences discussing why Francisco's answer is incorrect.
Francisco's answer is incorrect because the number of relative extrema a polynomial of degree five can have is at most four, not five. This is because a polynomial of degree five can have a maximum of four turning points, including both local maxima and local minima.
Well, Francisco's answer is incorrect because a polynomial of degree five can have at most four relative extrema. The number of relative extrema is determined by the degree of the polynomial minus one. So in this case, it would be 5 - 1 = 4. Francisco seems to have created some extra extrema, maybe to make friends with the lonely number 5.
Francisco's answer is incorrect because the number of relative extrema of a polynomial of degree five is not always five. The number of relative extrema can be any number between zero and four, inclusive, depending on the shape and behavior of the polynomial.
Francisco's answer is incorrect because the number of relative extrema a polynomial of degree five can have is at most four. This is because the polynomial may have no relative extrema, or it may have one minimum followed by three maximums (or vice versa), but it cannot have exactly five.
