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Kapittel 6 · Ekstremalpunkterextrema · second-derivative test

The Second-Derivative Test: A Discriminant Decides

0:49Fortellerstemme
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Classifying a critical point with the Hesse matrix. Three cases shown side by side: a bowl (D > 0, f_xx > 0) is a local minimum; a dome (D > 0, f_xx < 0) is a local maximum; a saddle (D < 0) is neither. The discriminant D = f_xx · f_yy − f_xy² and the sign of f_xx read the verdict off the matrix.

Hesse matrixdiscriminantsecond-derivative testcritical pointlocal minimumlocal maximum