Definition. Let f be differentiable on an open interval I. The graph of f is concave upward on I if is increasing on the interval or is positive in the interval I.
The graph of f is concave downward on I if is decreasing on the interval of is negative in the interval I.
Definition. Let f be a function such that changes signs at x=c and f(c) is defined, then we call (c,f(c)) to be the point of inflection. Note that if (c,f(c)) is a point of inflection of f, then either or is undefined.