Derivative Connections
f prime has a relative minimum when
f double prime changes from negative to positive
f prime has a relative maximum when
f double prime changes from positive to negative
f has a point of inflection when
f double prime changes sign
f has a point of inflection when
f double prime changes signs
f has a possible point of inflection when
f double prime equals 0 or DNE
f is concave down when
f double prime is negative
f prime is decreasing when
f double prime is negative
f is concave up when
f double prime is positive
f prime is increasing when
f double prime is positive
f has a relative min when
f prime changes from negative to positive
f has a relative max when
f prime changes from positive to negative
f has a point of inflection when
f prime has a relative extreme
f has a critical point when
f prime is 0 or DNE
f is concave down when
f prime is decreasing
f is concave up when
f prime is increasing
When f is decreasing
f prime is negative
When f is increasing
f prime is positive
