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 153

Step 4: Set up a table.

INTERVALS (−∞,1) X= 1 (1,∞)

Test Point 0 2

f′′(x) − undefined −

f(x) concave no change concave

downward of concavity downward

Note that sincef(x) has no change of concavity atx=1,f does not have a point

of inflection.

Step 5: Write a conclusion.
Therefore, f(x) is concave downward on (−∞,∞) and has no point of inflection.
(See Figure 8.2-24.)

[–3, 5] by [–1, 4]

Figure 8.2-24

Example 5

The graph of f is shown in Figure 8.2-25, and f is twice differentiable. Which of the
following statements is true?

y

f

05 x

Figure 8.2-25

(A) f(5) < f′(5) < f′′(5)

(B) f′′(5)< f′(5) < f(5)

(C) f′(5)< f(5) < f′′(5)

(D) f′(5)<f′′(5)< f(5)