Newton’s Method With Error Checking

This program uses Newton’s Method to find the Zeros or roots of a function. Unlike other Newton’s Method programs this one to have a few special touches to it that make it worthwhile. First, the program displays the equation (Y1) upon loading. After asking for an X value to be the starting point, the calculator tests that value. If the derivative of Y1 at that value returns an answer of zero (thus making Newton’s method [x – f(x)/f'(x)] divide by zero), the calculator will display “Pathological Error: d/dx = 0.” If that X value does not immediately return a derivative of zero, after 50 unsuccessful iterations the calculator will assume that there is a pathological error, and will display the same error message as before. The typical Newton iteration program will continuously attempt iterations before the “divide by zero” error is displayed (if it ever is), wasting both time and batteries.