Try different initial guess values for the function in question 3 as well as some more of your own creation. Discuss whether Newton's method always works efficiently. If not, describe two possible situations where Newton's method fails to converge to a zero of the function, and explain why they fail to converge.

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Answer Problem 4...Please don't reject this question!!!

Problem 3
Use the following guidance to implement Newton's method in an Excel spreadsheet to find the
approximate root other than 0 for f (x) = 6x5 - x3 + 3x? with the initial guess x, = -5. Give your
answer accurate to 6 decimal places.
EXCEL:
Suppose we put our first guess in box Al. We will put the initial guess and subsequent guesses in
column A starting with A3 (just to leave room for labels).
We can then put the value of f(x) in column B and f"(x) in column C.
To do this we need to make the following entries:
A3 = A1
(this puts the starting guess xg in A3)
B3 = f(A3)
(this computes f(xo)
C3 = f(A3)
(this computes f'(xo))
A4 = A3 – B3/C3 (this applies the algorithm to get the new guess)
If you now copy A4 (not A3!) and B3 and C3 down the A, B and C columns, you have implemented
the algorithm.
You can change your starting guess by changing Al, and change your function by changing B3 and
C3 appropriately, and copying the results down.
Problem
Try different initial guess values for the function in question 3 as well as some more of your own
creation. Discuss whether Newton's method always works efficiently. If not, describe two possible
situations where Newton's method fails to converge to a zero of the function, and explain why they
fail to converge.
Transcribed Image Text:Problem 3 Use the following guidance to implement Newton's method in an Excel spreadsheet to find the approximate root other than 0 for f (x) = 6x5 - x3 + 3x? with the initial guess x, = -5. Give your answer accurate to 6 decimal places. EXCEL: Suppose we put our first guess in box Al. We will put the initial guess and subsequent guesses in column A starting with A3 (just to leave room for labels). We can then put the value of f(x) in column B and f"(x) in column C. To do this we need to make the following entries: A3 = A1 (this puts the starting guess xg in A3) B3 = f(A3) (this computes f(xo) C3 = f(A3) (this computes f'(xo)) A4 = A3 – B3/C3 (this applies the algorithm to get the new guess) If you now copy A4 (not A3!) and B3 and C3 down the A, B and C columns, you have implemented the algorithm. You can change your starting guess by changing Al, and change your function by changing B3 and C3 appropriately, and copying the results down. Problem Try different initial guess values for the function in question 3 as well as some more of your own creation. Discuss whether Newton's method always works efficiently. If not, describe two possible situations where Newton's method fails to converge to a zero of the function, and explain why they fail to converge.
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