2.1. Consider the bordered Hessian matrix obtained from the constrained opti- misation problem and answer the following questions about the matrix: 2x 2y 2x 12x? 0 2y (a) For which range of values of x and y would the matrix be positive definite? (b) For which range of values of x and y would the matrix be negative definite? (c) You are now told that the critical points (x*, y*) for the constrained optimi- sation problem were (-0.47,0.88) and (0.47, 0.88) respectively. Taking into consideration your answers in part (a) and (b) above, would you conclude that each of the critical points are a maximum, a minimum, or a saddle point? Explain.

2.1. Consider the bordered Hessian matrix obtained from the constrained opti- misation problem and answer the following questions about the matrix: 2x 2y 2x 12x? 0 2y (a) For which range of values of x and y would the matrix be positive definite? (b) For which range of values of x and y would the matrix be negative definite? (c) You are now told that the critical points (x, y) for the constrained optimi- sation problem were (-0.47,0.88) and (0.47, 0.88) respectively. Taking into consideration your answers in part (a) and (b) above, would you conclude that each of the critical points are a maximum, a minimum, or a saddle point? Explain.

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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