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​Suppose that the function f(x, y) has continuous partial derivatives fxx, fyy, and fxy at all...

​Suppose that the function f(x, y) has continuous partial derivatives fxx, fyy, and fxy at all points (x,y) near a critical points (a, b). Let D(x,y) = fxx(x, y)fyy(x,y) – (fxy(x,y))2 and suppose that D(a,b) > 0.

​(a) Show that fxx(a,b) < 0 if and only if fyy(a,b) < 0.

​(b) Show that fxx(a,b) > 0 if and only if fyy(a,b) > 0.
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