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 163

Answer: fhas a change of concavity atx=0. (See Figure 8.5-4.)

f′ incr. decr.

+ –

concave

upward

concave

downward

x

f′′

f

0

Figure 8.5-4

4. Find the values ofxwhere fhas a relative minimum. (See Figure 8.5-5.)

1

–2 0

f′(x)

x

y

Figure 8.5-5

Answer: fhas a relative minimum atx=−2. (See Figure 8.5-6.)

f′

x

f

• 2

0

decr. incr.

Figure 8.5-6

5. Givenf is twice differentiable, arrangef(10),f′(10),f′′(10) from smallest to
   largest. (See Figure 8.5-7.)

(^010)
y
x
f
Figure 8.5-7
Answer: f(10)=0,f′(10)>0 since fis increasing, andf′′(10)<0 since fis
concave downward. Thus, the order isf′′(10),f(10),f′(10).