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(b) Let f(x, y) ax² + bx²y + cy2 + d with a, b, c, d 0. By calculating fx, fy, fxx, fyy and fry, show that f(x, y) has a stationary point at (0, 0) and determine the conditions (in terms of a, b, c and d) under which this point is a maximum.

(b) Let f(x, y) ax² + bx²y + cy2 + d with a, b, c, d 0. By calculating fx, fy, fxx, fyy and fry, show that f(x, y) has a stationary point at (0, 0) and determine the conditions (in terms of a, b, c and d) under which this point is a maximum.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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(b) Let f(x, y) = ax² + bx²y + cy2 + d with a, b, c, d 0. By calculating fr, fy, fxx, fyy and fry, show that f(x, y) has a stationary point at (0, 0) and determine the conditions (in terms of a, b, c and d) under which this point is a maximum.
Transcribed Image Text:(b) Let f(x, y) = ax² + bx²y + cy2 + d with a, b, c, d 0. By calculating fr, fy, fxx, fyy and fry, show that f(x, y) has a stationary point at (0, 0) and determine the conditions (in terms of a, b, c and d) under which this point is a maximum.
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