Generalized local test for local extrema in single-variable functions

Authors

Eleftherios Gkioulekas, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

5-7-2013

Abstract

We give a detailed derivation of a generalization of the second derivative test of single-variable calculus which can classify critical points as local minima or local maxima (or neither), whenever the traditional second derivative test fails, by considering the values of higher-order derivatives evaluated at the critical points. The enhanced test is local, in the sense that it is only necessary to evaluate all relevant derivatives at the critical point itself, and it is reasonably robust. We illustrate an application of the generalized test on a trigonometric function where the second derivative test fails to classify some of the critical points.

Comments

Original published version available at https://doi.org/10.1080/0020739X.2013.790515

Recommended Citation

Eleftherios Gkioulekas (2014) Generalized local test for local extrema in single-variable functions, International Journal of Mathematical Education in Science and Technology, 45:1, 118-131, DOI: 10.1080/0020739X.2013.790515

Publication Title

International Journal of Mathematical Education in Science and Technology

DOI

10.1080/0020739X.2013.790515