find the points on curve that are almost equal

Question

How do I find the points pointed by the arrow in the graph. I.e. the points where the slope of curve is almost $0$.

Answer 1

If I understand you correctly, you are looking for values of $x$ at which the slope $f'(x)$ has a local maximum. If the function is second-differentiable, then a necessary condition for $x$ to be such a point is that $f''(x)=0$.