I have a curve, represented by a function $y = f(x)$, and a very special point $S$ on that curve. It is "special" in the following ways:
- the first derivative of $f(x)$ in the neighborhood of $S$ is positive
- the second derivative of $f(x)$ in the neighborhood of $S$ is negative, and has reached its maximum value
- the third derivative of $f(x)$ in the neighborhood of $S$ is zero
- the fourth derivative of $f(x)$ in the neighborhood of $S$ is negative
I've illustrated the function and its third derivative in the graph below. My question is, does this special point S on the blue curve have some meaningful name?
