For each of the following functions

f, use conditions 16.19 to 16.22 to classify the specified x as definitely local maximum, possibly local maximum, definitely local minimum, possibly local minimum, and/or definitely neither.

(a) f1x1, x22!31x122 - x1x2 + 1x222 - 11x1, x = 12, 12

(b) f1x1, x22! - 1x122 - 6x1x2 - 91x222, x = 1 -3, 12

(c) f1x1, x22!x1 - x1x2 + 1x222, x = 12, 12

(d) f1x1, x22!12x2 - 1x122 + 3x1x2 - 31x222, x = 112, 82

(e) f1x1, x22!x11x223, x = 10, 02

(f) f1x1, x22!6x1 + ln 1x12 + 1x222, x = 11, 32

(g) f1x1, x22!21x122 + 8x1x2 + 81x222 -

12x1 - 24x2, x = 11, 12

(h) f1x1, x22!41x122 + 3>x2 - 8x1 + 3x2, x = 11, 12