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