5 Steps to a 5 AP Calculus AB 2019 - William Ma

MA 3972-MA-Book April 11, 2018 17:21

Graphs of Functions and Derivatives 175

(b) The absolute maximum occurs at
x=2, since it is a relative maximum
and it is the only relative extremum on
(−1, 4). The absolute minimum occurs
atx=−1, since f(−1)< f(4) and the
function has no relative minimum on
[−1, 4].
(c) A change of concavity occurs atx=0.
However, f′(0) is undefined, which
impliesf may or may not have a
tangent atx=0. Thus, fmay or may
not have a point of inflection atx=0.
(d) Concave upward on (−1, 0) and
concave downward on (0, 4).
(e) A possible graph is shown in Figure 8.9-1.

(–1, 0)

0

1

2

–1 1 2 3 4

possible

point of

inflection

y

x

f

(4, 2)

Figure 8.9-1