Given the following polynomial find the maximum possible number of turning points. f(x)=x^14+x^6+x^9+x^3

Question

I'm not really sure how turning points work so could someone show me the steps along with the answer.

Answer 1

The maximum number of turning points for any polynomial is just the highest degree of any term in the polynomial, minus 1. You can see this easily if you think about how quadratic equations (degree 2) have one turning point, linear equations (degree 1) have none, and cubic equations (degree 3) have 2 turning points at most.

In this case, the highest degree is 14, so the maximum number of turning points is 13.

 

Hope this helps!