assume polynomial f has exactly two local maxes and one local min. what is the largest # of possible zeros of the function???
would it be 6 zeros?
To determine the largest number of possible zeros of a polynomial function with exactly two local maxima and one local minimum, we can use two important properties of polynomial functions:
1. The number of zeros is equal to the degree of the polynomial function.
2. The number of turning points (local maxima and minima) is equal to the degree minus one.
Let's denote the degree of the polynomial by 'n'.
Given that the function has exactly two local maxima and one local minimum, we know that the number of turning points (3) is equal to n - 1.
Since the number of turning points is equal to 3, we have:
n - 1 = 3.
Solving this equation for 'n', we find that n = 4.
Therefore, the largest possible number of zeros of the polynomial function is equal to the degree, which is 4.