Question

Given the polynomial P(x) = 6x^5 + 11x^4 - 179x^3 - 154x^2 + 120x How many max/min would you expect to see at most?

Option 1: 5
Option 2: 4
Option 3: 3
Option 4: 2

Answer 1

The polynomial P(x) is of the fifth degree, which means it can have at most 4 turning points, so the maximum number of extrema (maxima or minima) it can have is 3.

Step-by-step explanation:

The question asks how many maximum or minimum points (extrema) we would expect to see at most for the polynomial P(x) = 6x5 + 11x4 - 179x3 - 154x2 + 120x. The number of maxima or minima of a polynomial function is determined by its degree. A polynomial of degree n can have at most n-1 turning points, which means it can have up to n-2 extrema since turning points can be maxima or minima.

In this case, the polynomial is a fifth-degree polynomial, so it can have at most 5 - 1 = 4 turning points. Thus, the maximum number of maxima or minima the polynomial can have is 4 - 1 = 3. Therefore, the correct answer is Option 3: 3.