Question: Consider the function defined by (a) Find fx(x, y) and fy(x, y) for (x, y) (0, 0). (b) Use the definition of partial derivatives

Consider the function defined byf(x, y) = (xy(x - y) x + y 0, (x, y)


(a) Find fx(x, y) and fy(x, y) for (x, y) ≠ (0, 0).


(b) Use the definition of partial derivatives to find fx(0, 0) and fy(0, 0).


(c) Use the definition of partial derivatives to find fxy(0, 0) and fyx(0, 0).


(d) Using Theorem 13.3 and the result of part (c), what can be said about fxy or fyx?


= (0,0) (x, y) = (0, 0)*

f(x, y) = (xy(x - y) x + y 0, (x, y) = (0,0) (x, y) = (0, 0)*

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