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The first derivative test and the classification of stationary points

Published online by Cambridge University Press:  12 November 2024

Lorenzo Di Biagio
Lorenzo Di Biagio*
Affiliation:
Luiss ‘Guido Carli’, Viale Romania 32, 00197, Roma, Italy e-mail: [email protected]
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Extract

Given a real differentiable function f we say that a point x0 is a stationary point of f if f′ (x0) = 0.

In any standard single-variable calculus class, students learn how to determine the nature of a stationary point by checking the sign of f(x) in intervals to the left and to the right of the stationary point. In doing so, they are performing the first derivative test.

Type
Articles
Information
The Mathematical Gazette , Volume 108 , Issue 573 , November 2024 , pp. 407 - 418
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Copyright
© The Authors, 2024 Published by Cambridge University Press on behalf of The Mathematical Association

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References

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