The figure below shows the graph of $y=x$ together with the graph of

$$f(x)=x+2x^2.$$

- Show algebraically that zero is a fixed point of $f$.
- What happens if we iterate $f$ starting with a point really close to zero on the right?
- What happens if we iterate $f$ starting with a point really close to zero on the left?

Some folks would call zero a *neutral* fixed point. Does this make sense?