3. Consider the function f(x) 5 = 23 31 3° -x2 3 +13x+1 (a) Plot this function in Desmos. Use a viewing window with -2 ≤ x ≤ 6 and −14 ≤ y ≤ 19. On the same graph, plot the tangent line to y = f(x) at x = 1 and the tangent line at x = 3. (b) What will happen if you try to find a solution to f(x) = 0 with an initial guess of x0 = 1? Refer to your diagram to explain your answer. (Hint: Try doing the method for several iterations.) (c) Now use an initial guess of x0 = 5. Use Newton's method to find an approximate solution to f(x) = 0, by calculating 2. Give your answer to three decimal places. (d) Suggest an interval of values for the initial guess so that Newton's method will approach the middle x-intercept. Briefly explain your answer. [3 marks]
3. Consider the function f(x) 5 = 23 31 3° -x2 3 +13x+1 (a) Plot this function in Desmos. Use a viewing window with -2 ≤ x ≤ 6 and −14 ≤ y ≤ 19. On the same graph, plot the tangent line to y = f(x) at x = 1 and the tangent line at x = 3. (b) What will happen if you try to find a solution to f(x) = 0 with an initial guess of x0 = 1? Refer to your diagram to explain your answer. (Hint: Try doing the method for several iterations.) (c) Now use an initial guess of x0 = 5. Use Newton's method to find an approximate solution to f(x) = 0, by calculating 2. Give your answer to three decimal places. (d) Suggest an interval of values for the initial guess so that Newton's method will approach the middle x-intercept. Briefly explain your answer. [3 marks]
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
![3. Consider the function
f(x)
5
=
23
31
3°
-x2
3
+13x+1
(a) Plot this function in Desmos. Use a viewing window with -2 ≤ x ≤ 6 and −14 ≤ y ≤ 19. On
the same graph, plot the tangent line to y = f(x) at x = 1 and the tangent line at x = 3.
(b) What will happen if you try to find a solution to f(x) = 0 with an initial guess of x0 = 1? Refer
to your diagram to explain your answer.
(Hint: Try doing the method for several iterations.)
(c) Now use an initial guess of x0 = 5. Use Newton's method to find an approximate solution to
f(x) = 0, by calculating 2. Give your answer to three decimal places.
(d) Suggest an interval of values for the initial guess so that Newton's method will approach the
middle x-intercept. Briefly explain your answer.
[3 marks]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78d1386b-6fe1-438f-8c94-3f41a9b64a70%2Fb5d7c6b2-fd62-481b-97d6-3dee69201458%2Ffk2n9hd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Consider the function
f(x)
5
=
23
31
3°
-x2
3
+13x+1
(a) Plot this function in Desmos. Use a viewing window with -2 ≤ x ≤ 6 and −14 ≤ y ≤ 19. On
the same graph, plot the tangent line to y = f(x) at x = 1 and the tangent line at x = 3.
(b) What will happen if you try to find a solution to f(x) = 0 with an initial guess of x0 = 1? Refer
to your diagram to explain your answer.
(Hint: Try doing the method for several iterations.)
(c) Now use an initial guess of x0 = 5. Use Newton's method to find an approximate solution to
f(x) = 0, by calculating 2. Give your answer to three decimal places.
(d) Suggest an interval of values for the initial guess so that Newton's method will approach the
middle x-intercept. Briefly explain your answer.
[3 marks]
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