(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 For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 13E: Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii...
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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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