(1) Consider the function f(x, y) = x³ - 2xy - y². (i) Verify that (0,0) and (-2/3, 2/3) are the critical points of f. (ii) Compute the Hessian H(f) = farfyy-fry of f at each critical point of f. (iii) Locate a saddle point of f and a local maximum point of f.
(1) Consider the function f(x, y) = x³ - 2xy - y². (i) Verify that (0,0) and (-2/3, 2/3) are the critical points of f. (ii) Compute the Hessian H(f) = farfyy-fry of f at each critical point of f. (iii) Locate a saddle point of f and a local maximum point of f.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:(1) Consider the function f(x, y) = x³ - 2xy - y².
(i) Verify that (0,0) and (-2/3, 2/3) are the critical points of f.
(ii) Compute the Hessian H(f) = farfyy - fy of f at each critical point of f.
(iii) Locate a saddle point of f and a local maximum point of f.
(iv) Use a cmputer to sketch the level curve f(x, y) = 0 and indicate the regions of R²
where f(x, y) is positive and where it is negative.
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Step 1: Define the problem
VIEWStep 2: Calculate the first order partial derivatives of function f(x,y,z)
VIEWStep 3: Calculate the critical points
VIEWStep 4: Calculate the second order partial derivatives
VIEWStep 5: Calculate the Hessian at critical points
VIEWStep 6: Calculate the location of saddle point and local maximum point of f
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