Question

PLZ HELP
List the possible number of extrema for each type of polynomial.
a) 5th degree polynomial
b) 6th degree polynomial

Answer 1

To find extrema we take the derivative, equate it to zero and solve for x.
When we take the derivative of a 5th degree polynomial, we will get a 4th degree polynomial which will have 4 zeros. All 4 zeros could be real, or two of them could be real or none of them could be real (that is, all of them are complex). Note: complex roots always occur in conjugate pairs and so the number of complex roots should always be even. So the 4th degree derivative polynomial can have 4 roots, 2 roots, 0 roots and those are the possible number of extrema (0, 2, 4).

Answer 2

Can you figure out b) ?