![]() The eigenvalues are thus $\lambda = \pm 1$, being the roots of $\lambda^2 - 1 = 0$ $P_5$ is indeed a saddle point. Example 2 Determine the critical points and locate any relative minima, maxima and saddle points of function f defined by f(x, y) 2x 2 - 4xy y 4 2. Enter the function and press calculate button to find the critical points. ![]() The only dubious thing I can see is the introduction of the equation $\cot x = \cot y$ this appears problematic since (i.) the cotangent functions have singularities in $(-\pi, \pi)$ and (ii.) I can see no way to infer the values of $x$ and $y$ given by $P_1$- $P_5$ from this equation indeed, all it directly tells us is that $x = y$, $x = y \pi$ or $x = y -\pi$ on $(-\pi, \pi) \setminus \$ Critical/Saddle point calculator for f(x,y) A saddle point is a point on a boundary of a set, such that it is not a boundary point.
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