Test the functions in Exercises 65–68 for local maxima and minima and saddle points. Find each function’s value at these points. 65. . ƒ(x, y) = 2x3 + 3xy + 2y3 66. ƒ(x, y) = x3 + y3 - 3xy + 15 67. ƒ(x, y) = x3 + y3 + 3x2 - 3y2 68. ƒ(x, y) = x4 - 8x2 + 3y2 - 6y

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.6: Quadratic Functions
Problem 58E
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Test the functions in Exercises 65–68 for local maxima and minima and saddle points. Find each function’s value at these points.

65. . ƒ(x, y) = 2x3 + 3xy + 2y3

66. ƒ(x, y) = x3 + y3 - 3xy + 15

67. ƒ(x, y) = x3 + y3 + 3x2 - 3y2

68. ƒ(x, y) = x4 - 8x2 + 3y2 - 6y

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