Possible Number of Local Extrema Is it possible for a third-degree polynomial to have exactly on

Name: Possible Number of Local Extrema Is it possible for a third-degree polynomial to have exactly one local extremum? Can a fourth-degree polynomial have exactly two local extrema? How many local extrema can polynomials of third, fourth, fifth, and sixth degree have? (Think about the end behavior of such polynomials.) Now give an example of a polynomial that has six local extrema.
Uploaded: 2023-09-15T00:03:14-08:00
Duration: 1 min 43 s
Channel: Alexander Frasco
Description: Possible Number of Local Extrema Is it possible for a third-degree polynomial to have exactly one local extremum? Can a fourth-degree polynomial have exactly two local extrema? How many local extrema can polynomials of third, fourth, fifth, and sixth degree have? (Think about the end behavior of such polynomials.) Now give an example of a polynomial that has six local extrema.

Question

Brittany Stefanilo · Accepted Answer

1. A third-degree polynomial can have at most two local extrema. This is because its derivative

Question

Please give Ace some feedback