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.