Barrons AP Calculus

Concavity

The global  or  absolute of  a   function    on  [a,    b]  occurs  at  x    =  c    if 

    for all x   on  [a, b].

A   curve   is  said    to  be  concave     on  an  interval    (a, b)  if  the curve   lies    

    the tangent lines   at  each    point   in  the interval    (a, b). If      at  every   point

in an interval (a, b), the curve is concave . In Figure N4–1, the curves
sketched in (a) and (b) are concave downward, while in (c) and (d) they are
concave upward.

Figure  N4–1

A point of inflection is a point where the curve changes its concavity from
upward to downward or from downward to upward. See §I, for a table relating a
function and its derivatives. It tells how to graph the derivatives of f, given the
graph of f. In Chapter 4 and 6, we graph f, given the graph of f ′.