Using Java, write a program that finds the minimum or maximum value for the following function:

z = x^6 + 3y^3 - xy - x + 10

In order to find the min/max, use Newton-Raphson's method, with 1 < |x| < 10 and 1 < |y| 9. The initial x and y values can be anything within this range, and subsequent x values are found using

xn+1 = xn  f'(xn) / f''(xn)

and subsequent y values are found using

yn+1 = yn  f'(yn) / f''(yn)

You will know a min or max has been found when the difference between the new solution and previous solution is less than 0.00001 in 1000 iterations. Plug the final x and y into the original equation for z.