justifications

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f has a relative maximum when f' ______ and f'' is _______

0, decreasing

f has a relative minimum when f' ________ and f'' is _________

0, increasing

f has a point of inflection when f''

changes sign

f is concave down when f' is

decreasing

f has a relative maximum when f' changes

from positive to negative

f is concave up when f' is

increasing

If f' is decreasing what is f''?

negative

When f is decreasing then f' is

negative

relative minimum

negative to positive

If f' is increasing what is f''?

positive

when f is increasing, then f' is

positive

relative maxium

positive to negative

if f'' < 0

then f has a relative maximum

if f'' > 0

then f has a relative minimum


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