Suppose that f (x, y) has continuous second-order partialderivatives everywhere and that
Chapter 13, Problem 2(choose chapter or problem)
Suppose that \(f(x, y)\) has continuous second-order partial derivatives everywhere and that the origin is a critical point for f . State what information (if any) is provided by the second partials test if
(a) \(f_{x x}(0,0)=2, f_{x y}(0,0)=2, f_{y y}(0,0)=2\)
(b) \(f_{x x}(0,0)=-2, f_{x y}(0,0)=2, f_{y y}(0,0)=2\)
(c) \(f_{x x}(0,0)=3, f_{x y}(0,0)=2, f_{y y}(0,0)=2\)
(d) \(f_{x x}(0,0)=-3, f_{x y}(0,0)=2, f_{y y}(0,0)=2\)
Equation Transcription:
Text Transcription:
f(x,y)
f_xx (0, 0)=2, f_xy (0, 0)=2, f_yy (0, 0)=2
f_xx (0, 0)=-2, f_xy (0, 0)=2, f_yy (0, 0)=2
f_xx (0, 0)=3, f_xy (0, 0)=2, f_yy (0, 0)=2
f_xx (0, 0)=-3, f_xy (0, 0)=2, f_yy (0, 0)=2
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