Write a program implementing Newton’s method. The program should have a script f

Question

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

The Newton’s 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

Explanation / Answer

#include #include double F(double x) {//our function return ((x)*(x)-5); } double Fd(double x) {//function's differentiation return (2*(x)); } int main() { double x0,h,err,root,x1; int miter,iter; printf("Enter the first approximation ,the max error and the maximum number of iterations "); scanf("%lf%lf%d",&x0,&err,&miter); iter=1; while(iter

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