P(x) has two local maxima and one local minimum. Answer the following

[Painguy]

Homework Statement

Assume that the polynomial P(x) has exactly two local maxima and one local minimum, and that these are the only critical points of P(x). Sketch possible graphs of P(x) and use them to answer the following.
(e) What is the sign of the leading coefficient of P(x)?
positive
negative

The Attempt at a Solution

I'm not sure how to get the sign of the graph

 

[STEMucator]

Well think about it, your graph would go from a max, to a min, back to a max.

So by the time it was done, the graph would be heading towards negative infinity would it not?

So what does that tell you about the co-efficient of your first term?

 

[Painguy]

Well think about it, your graph would go from a max, to a min, back to a max.

So by the time it was done, the graph would be heading towards negative infinity would it not?

So what does that tell you about the co-efficient of your first term?

ooooo haha well that's silly of me. For some reason I had the image of a sine graph stuck in my mind. That makes perfect sense thank you.