AP Calc Unit 4

the function f is increasing because f’

> 0 (is positive)

the function f is decreasing because f’

_{< 0 (is negative)}

the function f has a relative maximum because f’

changes from positive to negative

the function f has a relative maximum because f’’

f’ = 0

f’’ < 0

the function f has a relative minimum because f’

changes from negative to positive

the function f has a relative minimum because f’’

f’ = 0

f’’ > 0

the function f is concave up because f’ is

increasing

the function f is concave up because f’’ is

> 0 (is positive)

the function f is concave down because f’ is

decreasing

the function f is concave down because f’’ is

< 0 (is negative)

the function f has an inflection point because f’ has

relative extrema (changes from increasing to decreasing and vice versa)

the function f has an inflection point because f’’

changes sign