Let

(a) Graph f.

(b) Find f_x(x, y) and f_y(x, y) when (x, y) ≠ (0, 0).

(c) Find f_x(0, 0) and f_y(0, 0) using Equations 2 and 3.

(d) Show that f_xy(0, 0) = −1 and f_yx(0, 0) = 1.

(e) Does the result of part (d) contradict Clairaut’s Theorem? Use graphs of f_xy and f_yx to illustrate your answer.

Transcribed Image Text:

(x'y– xy³ x² + y? if (x, y) + (0, 0) 2 f(x, y) = if (x, y) = (0, 0)