The function of 2 variables f(x,y) has a stationary point with a Hessian Matrix: H = [1 -2] [-2 2] How would you describe this stationary point? - local minimum, local maximum, saddle point or that it cannot be determined from the Hessian Matrix?

The function of 2 variables f(x,y) has a stationary point with a Hessian Matrix: H = [1 -2] [-2 2] How would you describe this stationary point? - local minimum, local maximum, saddle point or that it cannot be determined from the Hessian Matrix?

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

The function of 2 variables f(x,y) has a stationary point with a Hessian Matrix:

H =

[1 -2]
[-2 2]

How would you describe this stationary point?
- local minimum, local maximum, saddle point or that it cannot be determined from the Hessian Matrix?

Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .

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