Question

Given the function f(x) = n^7 + 5n^10 + n^8 + n there are at most ___ x intercepts and at most ___ turning points

Can someone teach me what to look for please?

Answer 1

Would it be 10 x intercepts and 4 turning points?

Answer 2

I don't know if I'm looking at it correctly or have to look for something else

Answer 3

Turning points would be 9 right; all I have to do is 10-1?
Someone correct me if wrong

Answer 4

yes, there at most 9 turning points and 10 x-intercepts.

This particular polynomial only has 1 turning point, however, since its derivative only has one root. And it has but two x-intercepts.