BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 2.4, Problem 21E

a.

To determine

To find: the average rate of change of the function.

Expert Solution

Answer to Problem 21E

The average rate of change is 12

Explanation of Solution

Given information:

The linear function is f(x)=12x+3 and value of the variables is x=a and x=a+h

Formula used:

  f(x2)f(x1)f2f1

Calculation:

Substitution of f(a) and f(a+h)

  f(a)=12a+3f(a+h)=12(a+h)+3             =12a+12h+3

Therefore, the average rate of change:

  f(a+h)f(a)(a+h)a=12a+12h+312a3h                            =12hh                            =12

Hence, the average rate of change is 12

b.

To determine

To show: the average rate of change is the same as the slope of the line.

Expert Solution

Explanation of Solution

Given information:

The linear function is f(x)=12x+3 and value of the variables is x=a and x=a+h

Formula used:

Standard equation of line in Slope-intercept form is:

  y=mx+c

Proof:

Compare f(x)=12x+3 with y=mx+c ,

Therefore, the slope of line is

  m=12

Hence, the slope of line is m=12

So, both the slope and average rate of change is same.

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