Q:

Polynomial and convex functions

Consider polynomials $\mathbb{R} \rightarrow \mathbb{R}$. I have to

Give an example of polynomial that isn't convex downward nor convex upward.
Give an example of polynomial that is convex downward and convex upward
Explain why polynomial with degree 2 is convex downward or convex upward

3.I would say that $(ax^2 + bx + c)^{''}=2a$, $a \neq 0$ so $2a < 0$ or $2a > 0$
but how to do 1. and 2.?

A:

A higher degree polynomial that has a convex downward and convex upward part. You can try to construct a third degree polynomial with 3 roots.
A line.

