AP Calc Chapter 4

if f'(x) is > 0

f(x) is increasing

if f'(x) is <0

f(x) is decreasing

if f"(x) is >0

f(x) is concave up, min

if f"(x) is <0

f(x)is concave down, max

If f'(x) = 0 or undefined and changes sign from POS to NEG

relative MAX

If f'(x)=0 or undefined and changes sign from NEG to POS

relative min

If f'(x)=0 or undefined but DOES NOT CHANGE signs

critical point

if f"(x)=0 and changes sign

inflection point