Find a function with 4 unstable fixed points

Question

I need to find a function that has 4 fixed points, and all of them are unstable. I don't know how to proceed in this kind of problem, but i know how to find the fixed points in a function, and i know how to determine if the fixed points are unstable or stable, but i never worked constructing a function with $n-$fixed points. I think there is a general way to make those functions, but i don't know it.

Any hints?

Answer 1

Hint: Try $f$ of the form $f(x) = x + c (x-x_1)(x-x_2)(x-x_3)(x-x_4)$. Now what do you need to be sure that $x_1, \ldots, x_4$ are unstable?