(x, y) = xy – x – 4y; Ris the triangular region with vertices (0, 0), (0, 16), and (4, 0) Absolute maximum: i Absolute minimum: i eTextbook and Media Hint Assistance Used A point (xo, yo) in the domain of a function f(x, y) is called a critical point of the function if f. (Xo, Yo) = 0 and f, (xo, Yo) = 0 or if one or both partial derivatives do not exist at (xo, Yo). The Second Partials Test: Letf be a function of two variables with continuous second-order partial derivatives in some disk centered at a critical point (xo, Yo), and let D = fu (xo- Yo )f»y (xo. Yo) – f5 (x0. Yo) (a) If D > 0 and f (xo, Yo) > 0, thenf has a relative maximum at (xo, Yo). (b) If D > 0 and fe« (xo, Yo) < 0, thenf has a relative minimum at (xo, Yo)- (c) If D < 0, thenf has a saddle point at (xo, yo)- (d) If D = 0, then no conclusion can be drawn.

(x, y) = xy – x – 4y; Ris the triangular region with vertices (0, 0), (0, 16), and (4, 0) Absolute maximum: i Absolute minimum: i eTextbook and Media Hint Assistance Used A point (xo, yo) in the domain of a function f(x, y) is called a critical point of the function if f. (Xo, Yo) = 0 and f, (xo, Yo) = 0 or if one or both partial derivatives do not exist at (xo, Yo). The Second Partials Test: Letf be a function of two variables with continuous second-order partial derivatives in some disk centered at a critical point (xo, Yo), and let D = fu (xo- Yo )f»y (xo. Yo) – f5 (x0. Yo) (a) If D > 0 and f (xo, Yo) > 0, thenf has a relative maximum at (xo, Yo). (b) If D > 0 and fe« (xo, Yo) < 0, thenf has a relative minimum at (xo, Yo)- (c) If D < 0, thenf has a saddle point at (xo, yo)- (d) If D = 0, then no conclusion can be drawn.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.4: Definition Of Function

Problem 61E

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