Mathematics Homework Help. CSULA Optimality Conditions for Various Functions Questions
Please explain how to tackle this problem.
Show that the function f(x) = 8×1 + 12×2 + x21 − 2×22 has only one stationary point, and that it is neither a local maximizer nor a local minimizer, but a saddle point (which means the Hessian has both positive and negative eigenvalues).
(b) Show that the 2-dimensional function f(x1,x2) = (x2−x21)2−x21 has only one stationary point, which is neither a local maximizer nor a local minimizer, but a saddle point.
(c) Find all the critical points of the 2-dimensional function f(x1,x2) = (x21 − 1)2 + x22. Which are local minimizers? Which are not local minimizers?
(d) Find all the critical points of the 2-dimensional function f(x1,x2) = (x21−1)2+(x22−1)2. Which are local minimizers? Which are not local minimizers?
