EXAMPLE 25A
Given the graph of f (x) shown in Figure N4–12, sketch f ′(x).
FIGURE N4–12Point x = Behavior of f Behavior of f ′c 1 f (c 1 ) is a local max f^ ′(c^1 ) = 0; f^ ′ changes sign
from + to −c 2c 2 is an inflection point of f; the
graph of f changes concavity
from down to upf ′ changes from decreasing
to increasing; f ′(c 2 ) is a
local minimumc 3 f (c 3 ) is a local minimum f^ ′(c^3 ) = 0; f^ ′ changes sign
from − to +c 4c 4 is an inflection point of f; the
graph of f changes concavity
from up to downf ′ changes from increasing
to decreasing; f ′(c 4 ) is a
local maximumc 5 f (c 5 ) is a local maximum f^ ′(c^5 ) = 0; f^ ′ changes sign
from + to −