Question

What is the maximum number of possible extreme values for the function f(x)=x^4+x^3-7x^2-x+6

A. 3
B. 4
C. 5
D. 2

Answer 1

A 4th degree polynomial will have at most 3 extreme values. Since the degree is even, there will be one global extreme, with possible multiplicity. The remainder, if any, will be local extremes that may be coincident with each other and/or the global extreme.

(The number of extremes corresponds to the degree of the derivative, which is 1 less than the degree of the polynomial.)