Write a program in which you define a function, input an initial guess, and implement Newton's Method. Your output should record each guess and the value of the function at the guess. Stop when two consecutive guesses are within 10 or after 15 steps. As usual, the program and the output should be imported into SWP. Evaluate your results. Values should be shown with 15 digit accuracy. Run the program for the following: 1.f(x)=x-10x+22x+6. Start with an initial guess of x=2. What goes wrong? Try another guess. 2.f(x)=179.53x-436.85x+257.32x-0.001. Find all three positive roots.