Abstract
We derive, using critical points and the Hessian, a method of locating local maxima, local minima and saddle points of a real-valued function defined on an open subset of \({\mathbb R}^n\).
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Notes
- 1.
The notation \(\nabla ^{2}(f)\) is also used for the Hessian of \(f\).
- 2.
We could refocus this analysis to show that any symmetric \(n\times n\) matrix with real entries admits eigenvalues.
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© 2014 Springer-Verlag London
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Dineen, S. (2014). Maxima and Minima on Open Sets. In: Multivariate Calculus and Geometry. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-1-4471-6419-7_4
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DOI: https://doi.org/10.1007/978-1-4471-6419-7_4
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Publisher Name: Springer, London
Print ISBN: 978-1-4471-6418-0
Online ISBN: 978-1-4471-6419-7
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