Question

The graph of y​ = 5x^6 - 3x^4 + 2x - 9 has at most how many turning​ points?

Answer 1

Answer:

5

Step-by-step explanation:

The polynomial given is:

$y=5x^6 - 3x^4 + 2x - 9$

What is the degree of the polynomial?

The degree is the "highest" power of x in the polynomial.

6th power of x

4th power of x

1st power of x

All in the polynomial.

But the HIGHEST degree is 6th, so we call this a 6th order, or 6th degree polynomial.

Now,

Turning Point is the point on the graph where graph changes from increasing to decreasing or decreasing to increasing.

The general rule is that the max number of turning points of a polynomial is "1 less than the degree of the polynomial".

This is a 6th degree polynomial, so AT MOST there can be 5 turning points of the graph.