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

MA 3972-MA-Book May 8, 2018 13:46

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

Example 5

Solve 3 ln 2x=12 to the nearest thousandth.

3ln2x= 12

ln 2x = 4

eln 2x =e^4

2 x =e^4

x =

e^4

2

= 27. 299

5.4 Graphs of Functions

Main Concepts:Increasing and Decreasing Functions; Intercepts and Zeros; Odd and

Even Functions; Shifting, Reflecting, and Stretching Graphs

Increasing and Decreasing Functions

Given a functionf defined on an interval:

• f is increasing on an interval if f(x 1 )< f(x 2 ) wheneverx 1 <x 2 for anyx 1 andx 2 in
  the interval.


• f is decreasing on an interval if f(x 1 )> f(x 2 ) wheneverx 1 <x 2 for anyx 1 andx 2 in
  the interval.


• fis constant on an interval if f(x 1 )= f(x 2 ) for anyx 1 andx 2 in the interval.
  A function value f(c) is called arelative minimumof f if there exists an interval (a,b)in
  the domain offcontainingcsuch that f(c)≤f(x) for allx∈(a,b).
  A function valuef(c) is called arelative maximumoffif there exists an interval (a,b)
  in the domain off containingcsuch that f(c)≥ f(x) for allx∈(a,b).
  (See Figure 5.4-1.)

Absolute

minimum

Relative

maximum

Decreasing

Decreasing

Increasing Constant

0

y

f(x)

x

Figure 5.4-1

See the following examples. Using your graphing calculator, determine the intervals

over which the given function is increasing, decreasing, or constant. Indicate any relative

minimum and maximum values of the function.