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 165

7. Given the graph of f′′in Figure 8.6-2,
   determine the values ofxat which the
   functionfhas a point of inflection.
   y

a c x

f′′

(^0) b
Figure 8.6-2

8. Iff′′(x)=x^2 (x+3)(x−5), find the values
   ofxat which the graph of fhas a change of
   concavity.


9. The graph of f′on [−3, 3] is shown in
   Figure 8.6-3. Find the values ofxon
   [−3, 3] such that (a)fis increasing and
   (b)f is concave downward.
   y

x

• 33210

f′

Figure 8.6-3

10. The graph offis shown in Figure 8.6-4
    and fis twice differentiable. Which of the
    following has the largest value?

(a) f(−1)

(b) f′(−1)

(c) f′′(−1)

(d) f(−1) and f′(−1)

• 10

f

y

x

Figure 8.6-4

Sketch the graphs of the following functions

indicating any relative and absolute

extrema, points of inflection, intervals on

which the function is increasing, decreasing,

concave upward, or concave downward.

11. f(x)=x^4 −x^2


12. f(x)=
    x+ 4
    x− 4

Part B Calculators are allowed.

13. Given the graph off′in Figure 8.6-5,
    determine at which of the four values ofx
    (x 1 ,x 2 ,x 3 ,x 4 )fhas:
    (a) the largest value.
    (b) the smallest value.
    (c) a point of inflection.
    (d) and at which of the four values ofx
    doesf′′have the largest value.

f′

x 1 x 4

x

y

(^0) x 2 x 3
Figure 8.6-5