Order of polynomial $n$th derivative decrements each time the derivative is taken
-### Maxima and minima
+### Points of Inflection
-- if $f^\prime (a) = 0$ and $f^{\prime\prime}(a) > 0$, then point $(a, f(a))$ is a local min (curve is concave up)
+*Point of inflection* - point of maximum gradient (either +ve or -ve). Occurs where $f^{\prime\prime} = 0$
+- if $f^\prime (a) = 0$ and $f^{\prime\prime}(a) > 0$, then point $(a, f(a))$ is a local min (curve is concave up)
- 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
-*Point of inflection* - point of maximum gradient (either +ve or -ve)
+
## Antidifferentiation