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1. Consider the function f(x) = r³ - 3r² +3. (a) Using Newton's method up to 5 iterations, approximate the zeros of f(x)
Posted: Thu Jun 30, 2022 7:39 pm
by answerhappygod
- 1 Consider The Function F X R 3r 3 A Using Newton S Method Up To 5 Iterations Approximate The Zeros Of F X 1 (55.32 KiB) Viewed 33 times
1. Consider the function f(x) = r³ - 3r² +3. (a) Using Newton's method up to 5 iterations, approximate the zeros of f(x) for each of the following different initial approximations 20. Your answer should include a plot of f(r) along with (25, 0), as well as the equations you used. i. 201 = ii. To - 4 iii. To = -1/1 (b) Notice that in the previous problem, the method with initial approximation to = / did not converge to the closest root. Explain in your own words why this occurred, and use plots to justify your answer (HINT: Look at the tangent lines of f at ₁ and ₂). - (c) Notice that Newton's method fails with an initial approximation of ro= 2. Graph the tangent line of f atxo = 2 and give 2 reasons why Newton's method fails. (HINT: one reason should focus on the graph of the tangent line, the other reason should focus on the algorithm itself).