Suppose is a Function of which is twice Differentiable at a Stationary Point .
If is a 2-D Function which has a Relative Extremum at a point and has
Continuous Partial Derivatives at this point, then
. The second Partial Derivatives test classifies
the point as a Maximum or Minimum. Define the Discriminant as
See also Discriminant (Second Derivative Test), Extremum, Extremum Test, First Derivative Test, Global Maximum, Global Minimum, Hessian Determinant, Maximum, Minimum, Relative Maximum, Relative Minimum, Saddle Point (Function)
Abramowitz, M. and Stegun, C. A. (Eds.).
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.
New York: Dover, p. 14, 1972.