218 Chapter 3: Applications of Differentiation
3.8 Newton’s Method
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Complete two iterations of Newton‘s Method for the function using the
initial guess . Round your answers to four decimal places.
a.
b.
c.
d.
e.
____ 2. Complete two iterations of Newton’s Method for the function using the
initial guess . Round all numerical values in your answer to four decimal places.
a.
b.
c.
d.
3.8 Newton’s Method 219
e.
____ 3. Use Newton´s Method to approximate the zero(s) of the function
accurate to three decimal places.
a.
b.
c.
d.
e.
____ 4. Use Newton’s Method to approximate the zero(s) of the function
accurate to three decimal places.
a.
b.
c.
d.
e.
____ 5. Use Newton’s Method to approximate the zero(s) of the function
accurate to three decimal places.
a.
b.
c.
d.
e.
220 Chapter 3: Applications of Differentiation
____ 6. Approximate the positive zero(s) of the function to three decimal
places. Use Newton’s Method and continue the process until two successive approximations differ by
less than 0.001.
a.
b.
c.
d.
e.
____ 7. Use Newton´s Method to approximate the x-value of the indicated point of
intersection of the two graphs accurate to three decimal places. Continue the process until two
successive approximations differ by less than 0.001. [Hint: Let .]
a.
b.
c.
d.
e.
3.8 Newton’s Method 221
____ 8. Apply Newton’s Method to approximate the x-value of the indicated point of
intersection of Continue the process until two successive approximations
differ by less than 0.001. [Hint: Let .] Round your answer to three decimal places.
a.
b.
c.
d.
e.
____ 9. Approximate the fixed point of the function between to two
decimal places. [A of a function f is a value of x such that .]
a.
b.
c.
d.
e.
____ 10. Find the point on the graph of that is closest to the point . Round
all numerical values of the solution to three decimal places.
a.
b.
c.
d.
e.
222 Chapter 3: Applications of Differentiation
____ 11. Find the point on the graph of that is closest to the point . Use
Newton’s Method to approximate all numerical values of the solution to three decimal places.
a.
b.
c.
d.
e.
____ 12. The concentration C of a chemical in the blood-stream t hours after injection into
muscle tissue is given by When is the concentration greatest? Round your answer to
three decimal places.
a.
b.
c.
d.
e.
____ 13. Suppose that the total number of arrests T (in thousands) for all males ages 14 to 27
in 2006 is approximated by the model where x is
the age in years (see figure). Approximate the two ages to one decimal place that had total arrests of
thousand.
a.
b.
c.
d.
e.
3.8 Newton’s Method 223
____ 14. The total number of arrests T (in thousands) for all males ages 15 to 24 in 2010 is
approximated by the model T = 0.2988 – 22.625 + 628.49 – 7565.9x + 33478 for
where x is the age in years (see figure). Approximate the two ages that had total arrests of 340
thousand. Round all numerical values of the solution to two decimal places.
a. 17.99, 20.97
b. 17.75, 21.26
c. 17.99, 21.26
d. 17.75, 20.97
e. 20.78, 23.21
____ 15. You are in a boat 2 miles from the nearest point on the coast (see figure). You are to
go to a point Q that is 3 miles down the coast and 1 mile inland. You can row at 3 miles per hour and
walk at 5 miles per hour. Toward what point on the coast should you row in order to reach Q in the
least time?
a. x = 1.73
b. x = 1.43
c. x = 1.03
d. x = 0.93
e. x = 1.23
224 Chapter 3: Applications of Differentiation
3.8 Newton’s Method
Answer Section