Question: Consider the function (a) Show that is continuous at the origin. (b) Show that x and y exist at the origin, but

Consider the function

f(x, y) = 3xy.

(a) Show that ƒ is continuous at the origin.

(b) Show that ƒx and ƒy exist at the origin, but that the directional derivatives at the origin in all other directions do not exist.

(c) Use a computer algebra system to graph ƒ near the origin
to verify your answers in parts (a) and (b). Explain.

f(x, y) = 3xy.

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