Suppose you attempt to use Newton's method to approximate a solution of the equation x² + 5x³+4x² - 17x + 17 = 0. Let o 1 be the initial approximation, and then calculate x1, x2, x3, and x4. If a value is undefined, enter DNE. x1 = x2 = x3 = X4 = What do you notice? O Newton's method fails because f'(x) 0 but f(x) = 0. O Newton's method is successful at approaching a number so far. O Newton's method fails because the approximations are getting larger in absolute value. O Newton's method fails because the approximations are alternating between two numbers. =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Suppose you attempt to use Newton's method to approximate a solution of the equation
x² + 5x³ + 4x² 17x + 17 = 0.
4
Let ïð = 1 be the initial approximation, and then calculate î1, X2, X3, and x. If a value is
undefined, enter DNE.
x1 =
x2
x3
X4
=
-
=
What do you notice?
O Newton's method fails because f'(x) = 0 but ƒ(x) ‡ 0.
Newton's method is successful at approaching a number so far.
Newton's method fails because the approximations are getting larger in absolute value.
O Newton's method fails because the approximations are alternating between two numbers.
Transcribed Image Text:Suppose you attempt to use Newton's method to approximate a solution of the equation x² + 5x³ + 4x² 17x + 17 = 0. 4 Let ïð = 1 be the initial approximation, and then calculate î1, X2, X3, and x. If a value is undefined, enter DNE. x1 = x2 x3 X4 = - = What do you notice? O Newton's method fails because f'(x) = 0 but ƒ(x) ‡ 0. Newton's method is successful at approaching a number so far. Newton's method fails because the approximations are getting larger in absolute value. O Newton's method fails because the approximations are alternating between two numbers.
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