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Given the function below f(x, y, z) = 2 cos (r) + xy - xz - y² - e²% +2% (a) Show that the origin (0, 0, 0) is a stationary point (show the gradient is 0).

Given the function below f(x, y, z) = 2 cos (r) + xy - xz - y² - e²% +2% (a) Show that the origin (0, 0, 0) is a stationary point (show the gradient is 0).

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 70EQ
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Given the function below f(r, y, z) = 2 cos (r) + xy - xz – y – e2 + 2z %3D | (a) Show that the origin (0,0,0) is a stationary point (show the gradient is 0). (b) Show that the Hessian matrix ("second derivative matrix") at that point is -2 1 -1 H = 1 -2 -1 0 -4 (c) What kind of stationary point is this? Or is there insufficient information? Justify your answer.
Transcribed Image Text:Given the function below f(r, y, z) = 2 cos (r) + xy - xz – y – e2 + 2z %3D | (a) Show that the origin (0,0,0) is a stationary point (show the gradient is 0). (b) Show that the Hessian matrix ("second derivative matrix") at that point is -2 1 -1 H = 1 -2 -1 0 -4 (c) What kind of stationary point is this? Or is there insufficient information? Justify your answer.
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