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

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

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

8.5 Rapid Review

1. Iff′(x)=x^2 −4, find the intervals where fis decreasing. (See Figure 8.5-1.)

y

• 2 20 x
  
  
  • 4
  
  
  
  

f′(x)

Figure 8.5-1

Answer:Sincef′(x)<0if− 2 <x<2,f is decreasing on (−2, 2).

2. Iff′′(x)= 2 x−6 andf′is continuous, find the values ofxwhere fhas a point of
   inflection. (See Figure 8.5-2.)

3

concave

downward

concave

upward

Point of inflection

f′′

f

x

+

Figure 8.5-2

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

3. Find the values ofxwhere fhas change of concavity. (See Figure 8.5-3.)
   
   
   • 220
   
   
   
   

5

y

x

f′(x)

Figure 8.5-3