Stability of a Fixed Point Homework Help

Question

Determine the stability of all the fixed points of the following function: $f(x)=2\sin(x)$.

I've found the fixed points. They are $x=0$ and $x=1.895$. How can I determine the stability now?

Answer 1

When you evaluate $f$ at values of $x$ near your fixed points, does $f$ move toward or away from your fixed points? Look at the behavior of the derivative of $f$ to see what the slope is doing near those points.