Consider the following function:f(x, y) = xy(x2 y2)x2 + y2 , (x, y) = (0, 0),0, (x, y) =
Chapter 14, Problem 19(choose chapter or problem)
Consider the following function:f(x, y) = xy(x2 y2)x2 + y2 , (x, y) = (0, 0),0, (x, y) = (0, 0).The graph of f is shown in Figure 14.68, and the contourdiagram of f is shown in Figure 14.69.(a) Find fx(x, y) and fy(x, y) for (x, y) = (0, 0).(b) Show that fx(0, 0) = 0 and fy(0, 0) = 0.(c) Are the functions fx and fy continuous at (0, 0)?(d) Is f differentiable at (0,0)?
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