Relationships between f, f prime and f double prime
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when f'(x) is decreasing, f is
concave down; f'' is negative
when f'(x) is increasing, f is
concave up; f'' is positive
relative min of f occurs when f'..
crosses x axis (negative--positive)
relative max of f occurs when f'..
crosses x axis (positive--negative)
function decreasing when f'..
is negative (below x axis)
function is concave down when f''..
is negative (below x axis)
function increasing when f'..
is positive (above x axis)
function is concave up when f''..
is positive (above x axis)
function has a POI when f' is
a max/min OR when f' changes direction (inc-dec/dec-inc)