- if $f^\prime (a) = 0$ and $f^{\prime\prime} (a) < 0$, then point $(a, f(a))$ is local max (curve is concave down)
- if $f^{\prime\prime}(a) = 0$, then point $(a, f(a))$ is a point of inflection
- - if also $f^\prime(a)=0$, then it is a stationary point of inflection
- if $f^\prime (a) = 0$ and $f^{\prime\prime} (a) < 0$, then point $(a, f(a))$ is local max (curve is concave down)
- if $f^{\prime\prime}(a) = 0$, then point $(a, f(a))$ is a point of inflection
- - if also $f^\prime(a)=0$, then it is a stationary point of inflection