For each of the following unconstrained NLPs, either verify that the given x is a stationary point of the objective function or give a direction

Δx that improves at x.

(a) min 1x122 + x1x2 - 6x1 - 8x2, x = 18, -102

(b) max 101x122 + 2 ln 1x22, x = 11, 22

(c) min 16x1 - x1x2 + 21x222, x = 13, 02

(d) max x1x2 - 8x1 + 2x2, x = 1 -2, 82