Question: (a) Show that the function f (x, y) = 3 xy is continuous and the partial derivatives f x and f y exist at the

(a) Show that the function f (x, y) = ³√xy is continuous and the partial derivatives f_x and f_y exist at the origin but the directional derivatives in all other directions do not exist.
(b) Graph f near the origin and comment on how the graph confirms part (a).

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