1. (a) Give a function for which only one iteration for Newton's method to converge to its exact root using any initial

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1 A Give A Function For Which Only One Iteration For Newton S Method To Converge To Its Exact Root Using Any Initial 1 (63.78 KiB) Viewed 58 times

1. (a) Give a function for which only one iteration for Newton's method to converge to its exact root using any initial guess. Provide argument for your answer. (b) Consider the following graph of a function f. The exact root is indicated by r in the graph. With initial iterate to = 2, show by plotting tangent lines in the graph, two iterations of Newton's method. What would happen if you wish to continue this iteration? Propose an initial iterate that would guarantee a convergence to the exact root and give a reasoning why your choice should work. 0.8 0.6 0.4 0.2 0 -0.2- -0.4 f(x) -0.60 r 0.5 1.5 2x 2.5 3 3.5