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
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77ccc228-61ae-45bc-bff3-36e89ce5abe9%2F2dea56cd-b89d-47c2-958e-23bebbf8c1cc%2Faludzc_processed.jpeg&w=3840&q=75)
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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