MAT 21C Lecture Notes - Lecture 23: Derivative Test, Saddle Point, Maxima And Minima
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MAT 21C Full Course Notes
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Announcements: m 11/28 from 3:10-4pm 204 art, w 11/30 6:10-8pm 6 olson, r 12/1 for 4:10-5pm 6 wellman. Let f (x, y) be de ned on a region r containing the point (a, b). An interior point of the domain of a function f (x, y) where both fx and fy are zero or where one or both of fx, fy do not exist is a critical point of f . The corresponding point (a, b, f (a, b)) on the surface z = f (x, y) is called a saddle point of the surface. The expression fxxfyy f 2 it as the determinant of the hessian of f . xy is called the discriminant of f . Theorem 11. (second derivative test for local extreme values) suppose that f (x, y) and its rst and second partial derivatives are continuous throughout a disk centered at (a, b) and that fx(a, b) = fy(a, b) = 0.
