In [26]:
load("/Users/vincentdouce/Dropbox/LWS_FTP/jupyter/hessienne/code_general.sage")
fonction Q : ****
paramètres généraux
| f | \(\left( x, y \right) \ {\mapsto} \ x^{4} + y^{4} - {\left(x - y\right)}^{2}\) |
| grad f= | \(\left[4 \, x^{3} - 2 \, x + 2 \, y, 4 \, y^{3} + 2 \, x - 2 \, y\right]\) |
| H= | \(\left(\begin{array}{rr} 12 \, x^{2} - 2 & 2 \\ 2 & 12 \, y^{2} - 2 \end{array}\right)\) |
points critiques
| ( | x | = | \(-1\) | ; | y | = | \(1\) | ) | \(\left(\begin{array}{rr} 10 & 2 \\ 2 & 10 \end{array}\right)\) |
| ( | x | = | \(1\) | ; | y | = | \(-1\) | ) | \(\left(\begin{array}{rr} 10 & 2 \\ 2 & 10 \end{array}\right)\) |
| ( | x | = | \(0\) | ; | y | = | \(0\) | ) | \(\left(\begin{array}{rr} -2 & 2 \\ 2 & -2 \end{array}\right)\) |
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