needs to be written in C#

(12%) Newtons method (roots). Newtons method or Newton-Raphson method of calculating a function / a polynomials roots is an easy way that uses only the knowledge of ECE 114 (for loop). Write a method Newtonsmethod that calculates (or attempt to calculate) a root from an initial guess.

You need to stop the for loop or while loop when x _n and x_n+1 are close (for example, if their difference is less than 1.0x10^-7. ) or when n is big, say bigger than 50, since you do not want to iterate forever. However, there is a validity check: you want to make sure f(x _n) 0; it would make no sense if f(x _n) = 100 and you call that a root.

Test your method with the polynomial x³ + x + 1 and the initial guess x = -1.; and also the polynomial x² - 3x + 2 and the initial guess x = 0. We do not try to calculate complex roots here.