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, Problem 61RE

a.

To determine

To find the average rate of change of f between x=0 and x = 2 and x=15 and x = 50

Expert Solution

Answer to Problem 61RE

The average rate of change of f between x=0 and x = 2 is 12 and of x=15 and x = 50 is 12 .

Explanation of Solution

Given: The given function is f(x)=12x6

Calculation:

  f(x)=12x6

  =f(50)f(15)5015=193235=383235=352(135)=12

We get,

  and f(2)=12(2)6           =16            =5

So we get ,

  f(2)=5

Hence the average rate of change

  =f(2)f(0)20=5(6)2=5+62=12

Hence the average of change of f between.

  x=0x=2 is 12

Now we find f(15)and f(50) as follows;

  f(15)=12(15)6        =15122        f(15) =32

So, we get

  f(15) =32

And

  f(50)=12(50)6        =256         =19

We get

  f(50) =19

Hence the average rate of change is,

  =f(50)f(15)5015=193235=383235=352(135)=12

Hence the average of change of f between.

  x=15x=50 is 12

b.

To determine

To check whether the two average rates of change found in part (a) is same or not? And also explain why or why not.

Expert Solution

Answer to Problem 61RE

a) Two average rates of change found in part (a) is same as 12 for this function. Since the rate of change between any two arbitrary points x=0 and x= a+h is 12. Because it is a linear function.

Explanation of Solution

  YES it appears that the average rate of change is always 12 for this function. Since the rate of change between any two arbitrary points x=0 and x= a+h is 12. Because it is a linear function.

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