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 22E

a.

To determine

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

Expert Solution

Answer to Problem 22E

The average rate of change is 4

Explanation of Solution

Given information:

The linear function is g(x)=4x+2 and value of the variables is x=a and x=a+h

Formula used:

  g(x2)g(x1)g2g1 where ab

Calculation:

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

  g(a)=4a+2g(a+h)=4(a+h)+2             =4a4h+2

Therefore, the average rate of change is obtained as:

  g(a+h)g(a)(a+h)a=4a4h+2+4a2h                            =4hh                            (simplify)                            =4            

Hence, the average rate of change is 4

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 g(x)=4x+2 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 g(x)=4x+2 with y=mx+c ,

Therefore, the slope of line is

  m=4

Hence, the slope of line is m=4

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

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