2326 TrueFalse Determine whether the statement is trueor false. Explain your answer. In
Chapter 13, Problem 25(choose chapter or problem)
True-False Determine whether the statement is true or false. Explain your answer. In these exercises, assume that \(f(x, y)\) has continuous second-order partial derivatives and that
\(D(x, y)=f_{x x}(x, y) f_{y y}(x, y)-f_{x y}^{2}(x, y)\)
If \(P\left(x_{0}, y_{0}\right)\) is a critical point of \(f\) , and if \(f\) is defined on a disk centered at \(P\) with \(D\left(x_{0}, y_{0}\right)>0\), then \(f\) has a relative extremum at \(P\).
Equation Transcription:
Text Transcription:
f(x,y)
D(x,y)=f_xx(x,y)f_yy(x,y)-f_xy ^2(x,y)
P(x_0,y_0)
f
f
P
D(x_0,y_0)>0
f
P
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