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Find and classify the local extrema of the function f(x, y) = 5xy - 7x² + 3x - 6y + 2.

Find and classify the local extrema of the function f(x, y) = 5xy - 7x² + 3x - 6y + 2.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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Problem 6.2 Extreme values - Calculations a) Find and classify the local extrema of the function f(x, y) = 5xy - 7x² + 3x − 6y + 2. b) Find and classify the local extrema of the function g(x, y) = 1- x² + y². c) For which values of the constant k does the Second Derivative Test guarantee that f(x,y) = x² + kxy + y² will have a saddle point at (0, 0)? A local minimum at (0, 0)? For which values of k is the Second Derivative Test inconclusive? Justify your answers.
Transcribed Image Text:Problem 6.2 Extreme values - Calculations a) Find and classify the local extrema of the function f(x, y) = 5xy - 7x² + 3x − 6y + 2. b) Find and classify the local extrema of the function g(x, y) = 1- x² + y². c) For which values of the constant k does the Second Derivative Test guarantee that f(x,y) = x² + kxy + y² will have a saddle point at (0, 0)? A local minimum at (0, 0)? For which values of k is the Second Derivative Test inconclusive? Justify your answers.
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