Write a program implementing Newtons method. The program should have a script file that calls the Newtons method function in a different file.

The Newtons method function should input a function, its derivative, a starting point, a tolerance, and a maximum number of iterations. Use your code to find the zeros of the functions below. For each function:

i) Find a suitable initial guess.

ii) Comment on how difficult this guess was to find.

iii) Analyze the convergence by plotting the error as a function of the number of iteration on an appropriate graph.

iv) Determine if the order of convergence you find in iii) is consistent with theory of section 2.4.

(a) f(x) = 2.4-5x3 + x + 1 = 0. (b) g(x)= 2 sin2x-sinx + 0.125 (c) h(x) = 15 1/15,-=0. 0. 15 es (1/15) e-8a