(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 -4 (c) What kind of stationary point is this? Or is there insufficient information? Justify

(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 -4 (c) What kind of stationary point is this? Or is there insufficient information? Justify

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

4. Given the function below
f (x, y, z) = 2 cos (x) + xy – xz – y? – e2% + 2z
(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
H
1
-2
-1
(c) What kind of stationary point is this? Or is there insufficient information? Justify
your answer.

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