5 Steps to a 5 AP Calculus BC 2019

134 STEP 4. Review the Knowledge You Need to Score High

Iff′′(x)= 2 x−6 andf′is continuous, find the values ofxwhere fhas a point of
inflection. (See Figure 7.6-2.)

3

0–

concave downward

concave upward

Point of Inflection

f′′

f

x

+

Figure 7.6-2

Answer:Thus, fhas a point of inflection atx=3.

(See Figure 7.6-3.) Find the values ofxwhere f has change of concavity.

0–2 2

5

y

x

f′(x)

Figure 7.6-3

Answer: fhas a change of concavity atx=0. (See Figure 7.6-4.)

f′ incr. decr.

+– concave upward

concave downward

x f′′ f

0

Figure 7.6-4

(See Figure 7.6-5.) Find the values ofxwhere f has a relative minimum.

1

–2 0

f′(x)

x

y

Figure 7.6-5