Explain using your own words how you can determine the amount of turning points​ (relative extrema) of any given polynomial. Please provide an example.

Answer 1

To determine the amount of turning points or relative extrema of a polynomial, you need to look at the degree of the polynomial. The degree tells you the highest power of the variable in the polynomial.

For example, let's consider a polynomial of degree 3: f(x) = 2x^3 - 3x^2 + 4x + 1.

To determine the number of turning points or relative extrema, count the degree of the polynomial minus 1. In this case, the degree is 3, so we subtract 1 from 3: 3 - 1 = 2.

So, this polynomial will have 2 turning points or relative extrema.