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A more conclusive and more inclusive second derivative test

Published online by Cambridge University Press:  18 June 2020

Ronald Skurnick  and
Christopher Roethel
Ronald Skurnick
Affiliation:
Department of Mathematics, Computer Science and Information Technology, Nassau Community College, Garden City, New York11530USA
Christopher Roethel
Affiliation:
Department of Mathematics, Computer Science and Information Technology, Nassau Community College, Garden City, New York11530USA
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Given a differentiable function f with argument x, its critical points are those values of x, if any, in its domain for which either f′ (x) = 0 or f′ (x) is undefined. The first derivative test is a number line test that tells us, definitively, whether a given critical point, x = c, of f(x) is a local maximum, a local minimum, or neither. The second derivative test is not a number line test, but can also be applied to classify the critical points of f(x). Unfortunately, the second derivative test is, under certain conditions, inconclusive.

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Articles
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The Mathematical Gazette , Volume 104 , Issue 560 , July 2020 , pp. 247 - 254
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© Mathematical Association 2020

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References

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