f ff fff
when f'' changes sign
f has a POI
where f' has relative extrema
f has a POI
When f' changes from positive to negative
f has a relative max
When f' changes from negative to positive
f has a relative min
when f' is decreasing
f is concave down
when f'' is negative,
f is concave down
when f' is increasing
f is concave up
when f'' is positive,
f is concave up
when f' is negative
f is decreasing
when f' is positive,
f is increasing
When f has a horizontal tangent,
f' equals 0
where f'' changes from positive to negative,
f' has a relative max
where f'' changes from negative to positive
f' has a relative min
when f is concave down,
f' is decreasing
when f'' is negative,
f' is decreasing
when f is concave up,
f' is increasing
when f'' is positive,
f' is increasing
when f is decreasing,
f' is negative
When f is increasing,
f' is positive
When f has a point of inflection,
f'' has a change in sign
when f is concave down,
f'' is negative
when f is concave up,
f'' is positive
