Write a Newton method root-finding function. Remember that for the Newton methcnly need to give a single initial estimate, but you also need to supply the derivative. You can give both input function and its derivative as lambdas. 1. Use Newton's method to verify that the function h(x) = 4 tan-¹ x has a root at x = 0. 2. Try to find this root with a starting guess of xo = 1, and then with an starting guess of xo = 1.5. What goes wrong in the second case? 3. Now consider the function h(x) = x² - 2 (which clearly has a root at x = √2) with an initial guess of xo = 0. What is the problem?

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