Please feel free to use Matlab and show code.

Consider the following NLP min f(x) = x1 + x3 - 223 - 8x} 32x1 + 24.x2 (a) Analyze the critical point(s) for this problem. (b) Starting at x(0) = (1, 1) use the pure form of Newton's Method determine x(3), with the following caveat: if the search direction is NOT a descent direction, use the negative of the search direction instead. Feel free to create YOUR OWN code to do this problem in Matlab (or other software)