(a) local minimum, where $f(a)\leq f(a+h)\,$ for all $h$ with sufficiently small $|h|\,$;

(b) local maximum, where $f(a)\geq f(a+h)\,$ for all $h$ with sufficiently small $|h|\,$; and

(c) point of inflexion, where $f(a-h)<f(a)<f(a+h)\,$ or $f(a-h)>f(a)>f(a+h)$ for all $h>0$ sufficiently small. Local maxima and minima are generally interesting since the graph turns there, whereas inflexions are often merely curiosities.