Question

Do 4th degree polynomials have maxima and minima?
a. Yes
b. No

Answer 1

4th degree polynomials can have maxima and minima, with the possibility of up to three local extremums depending on the polynomial's coefficients.

correct option is a. Yes

Step-by-step explanation:

The question of whether 4th degree polynomials have maxima and minima can be answered with a yes. A 4th degree polynomial, also known as a quartic function, can have up to 3 local extremums, which means it can have a combination of local maximums and/or minimums. The exact number and nature of these maxima and minima depend on the specific coefficients of the polynomial.

However, since a 4th degree polynomial has a derivative which is a 3rd degree polynomial, which can have up to 2 critical points where the function's slope is zero, it can have up to two local maxima or minima. Besides, at the boundaries of its domain, a 4th degree polynomial may also have global maxima or minima.