3. Consider the root-finding problem f(x) = 9x² ² - 4x/5= 0 for x = [-1,1]; see figure (b). (a) With xo = 0, compute x₁, x2 using Newton's method for approximating the solution to this problem. (b) With xo = 0 and ₁= -0.5, compute p2 using the Secant method to approximate the solution to this problem. (c) Based on the plot of f(x), for what choice of xo will Newton's method converge to the desired root? Make sure to motivate you answer.
3. Consider the root-finding problem f(x) = 9x² ² - 4x/5= 0 for x = [-1,1]; see figure (b). (a) With xo = 0, compute x₁, x2 using Newton's method for approximating the solution to this problem. (b) With xo = 0 and ₁= -0.5, compute p2 using the Secant method to approximate the solution to this problem. (c) Based on the plot of f(x), for what choice of xo will Newton's method converge to the desired root? Make sure to motivate you answer.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![3. Consider the root-finding problem f(x) = ² - 4¹/5 = 0 for x = [−1, 1]; see figure (b).
(a) With xo = 0, compute x₁, x2 using Newton's method for approximating the solution to this
problem.
(b) With xo = 0 and x₁ = -0.5, compute p2 using the Secant method to approximate the solution to
this problem.
(c) Based on the plot of f(x), for what choice of zo will Newton's method converge to the desired
root? Make sure to motivate you answer.
(d) Based on the plot of f(x), for what choice of o, ₁ will the secant method not converge?
Make sure to motivate you answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1dbcb96-b484-476e-adb0-126482b446f4%2F6a787c1b-2f47-4cfd-83cf-5f25fbc5dffe%2Fmtwi5s_processed.png&w=3840&q=75)
Transcribed Image Text:3. Consider the root-finding problem f(x) = ² - 4¹/5 = 0 for x = [−1, 1]; see figure (b).
(a) With xo = 0, compute x₁, x2 using Newton's method for approximating the solution to this
problem.
(b) With xo = 0 and x₁ = -0.5, compute p2 using the Secant method to approximate the solution to
this problem.
(c) Based on the plot of f(x), for what choice of zo will Newton's method converge to the desired
root? Make sure to motivate you answer.
(d) Based on the plot of f(x), for what choice of o, ₁ will the secant method not converge?
Make sure to motivate you answer.
Transcribed Image Text:2.5
2
1.5
0.5
"
-1
-g(x)
-h(a)
1
0
X
(a) Plot of g(x) and h(x).
-0.5
0.5
0.5
0
-0.5
-1
-1.5
-0.5
0
X
0.5
(b) Plot of f(x) = 9x² - 4x/5
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