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

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

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

• 230 1 5

(–2, 10) (5, 6)

[ ] x

f

y

Figure 8.8-6

16. (a)

decr. incr. decr.

rel. min. rel. max.

• 
  
  
  
  • –
  
  
  
  

f^06

f′

The functionf has its relative

minimum atx=0 and its relative

maximum atx=6.

(b) The function fis increasing on [0, 6]

and decreasing on (−∞, 0] and [6,∞).

(c)

incr. decr.

+ –

concave

upward

concave

downward

pt. of

inflection

3

f′

f′′

f

Sincef′(3) exists and a change of

concavity occurs atx=3,fhas a

point of inflection atx=3.

(d) Concave upward on (−∞, 3) and

downward on (3,∞).

(e) Sketch a graph. (See Figure 8.8-7.)

036

(0, 1)

(6, 5)

x

y

f

Figure 8.8-7

17. (See Figure 8.8-8.)

[–5, 10] by [–5, 20]

Figure 8.8-8

The graph off indicates that a relative

maximum occurs atx=3,fis not

differentiable atx=7, since there is a cusp

atx=7 andf does not have a point of

inflection atx=−1, since there is no

tangent line atx=−1. Thus, only

statementIis true.