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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.

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

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References

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