Relative Extrema

if f' = 0 or DNE, f has...

a critical value

if f' changes from positive to negative, then f has...

a relative max

if f' changes from negative to positive, then f has...

a relative minimum

if f has a POI, then f''...

changes sign

if f has a POI, then the slope of f'...

changes sign

if f' is increasing, then f is....

concave up

if f'' is positive, then f is...

concave up

if f is concave up, then f' is...

increasing

if f' is positive, then f is

increasing

if f'' is positive, then f' is...

increasing

f has a critical value when f'...

is equal to zero or DNE

f has a relative maximum when f'' is...

negative

f has a relative minimum when f' changes from...

negative to positive

f has a relative minimum when f'' is...

positive

f is increasing when the graph of f' is...

positive

if f is concave up, then f'' is...

positive

if f' is increasing, then f'' is...

positive

f has a relative maximum when f' changes from...

positive to negative