Question: The function f(x)=(x-1)e has a double root at x = 1. (a) Derive Newton's iteration for this function. Show that the iteration is well-defined

The function f(x)=(x-1)e has a double root at x = 1. (a) Derive Newton's iteration for this function. Show that the iteration is well-defined so long as xk #-1 and that the convergence rate is expected to be similar to that of the bisection method (and certainly not quadratic). (b) Implement Newton's method and observe its performance starting from o = 2. (c) How easy would it be to apply the bisection method? Explain.

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