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The 2nd Derivative test
The second derivative test looks at the eigenvalues of the Hessian matrix evaluated at critical points.
The idea for this came from Ben Woodruff, who implemented a similar thing in Mathematica.
(x, y)
Critical Point | Eigenvalue | Eigenvector |
---|---|---|
(0.0, 0.0, 0.0) | -2.0 | (1.0, 0.0) |
(0.0, 0.0, 0.0) | 2.0 | (0.0, 1.0) |
Critical Point | Eigenvalue | Eigenvector |
---|---|---|
(0.0, 0.0, 0.0) | 1.0 | (0.707106781187, 0.707106781187) |
(0.0, 0.0, 0.0) | -1.0 | (-0.707106781187, 0.707106781187) |
(-1.22474487139, -1.22474487139, 0.551819161757) | -0.735758882343 | (0.707106781187, 0.707106781187) |
(-1.22474487139, -1.22474487139, 0.551819161757) | -0.735758882343 | (-0.707106781187, 0.707106781187) |
(1.22474487139, -1.22474487139, -0.551819161757) | 0.735758882343 | (0.707106781187, 0.707106781187) |
(1.22474487139, -1.22474487139, -0.551819161757) | 0.735758882343 | (-0.707106781187, 0.707106781187) |
(-1.22474487139, 1.22474487139, -0.551819161757) | 0.735758882343 | (0.707106781187, 0.707106781187) |
(-1.22474487139, 1.22474487139, -0.551819161757) | 0.735758882343 | (-0.707106781187, 0.707106781187) |
(1.22474487139, 1.22474487139, 0.551819161757) | -0.735758882343 | (0.707106781187, 0.707106781187) |
(1.22474487139, 1.22474487139, 0.551819161757) | -0.735758882343 | (-0.707106781187, 0.707106781187) |