AP Calc FUN chart + particle motion justifications

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f has a relative maximum when f' ____ and f" is ____

0 & negative

f has a relative minimum when f'_____ and f'' is _____

0 & positive

f has a point of inflection when f'

changes from increasing to decreasing or vice versa

f has a point of inflection when f''

changes sign

f is concave down when f' is

decreasing

f has a relative minimum when f' changes

from negative to positive

f has a relative maximum when f' changes

from positive to negative

f is concave up when f' is

increasing

f is concave down when f'' is

negative

f is decreasing when f' is

negative

f is concave up when f'' is

positive

f is increasing when f' is

positive

a particle is moving left when

v(t)<0

a particle is moving right when

v(t)>0


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