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Derivative test

In calculus, a derivative test uses the derivatives of a function to locate the critical points of a function and determine whether each point is a local maximum, a local minimum, or a saddle point. Derivative tests can also give information about the concavity of a function.

First-derivative test, Second-derivative test (single variable) & Multivariable case

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Overview

First-derivative test

Second-derivative test (single variable)

Multivariable case

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Derivative test

Nodes43
Edges42
Triples40
Avg. degree1.95
Density0.046512
Components1

How this topic connects Entity context

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Derivative test

Top relations

related to External links · 6
Derivative test → Convergence, Find Maxima, MathworldConcavity, Minima, Second Derivative Test, Second Derivative TestThomas Simpson's
related to First-derivative test · 5
Derivative test → However, If, One, Similarly, The
see also · 5
Derivative test → Bordered HessianConvex, Inflection, Kuhn, Phase, Tucker
related to Example · 4
Derivative test → As, Say, Thus, To
related to Higher-order derivative test · 4
Derivative test → Also, As, Let, The
related to Multivariable case · 4
Derivative test → For, Hessian, If, In
related to Precise statement of first-derivative test · 4
Derivative test → Further, It, Suppose, The
has application · 2
Derivative test → In, The
related to Second-derivative test (single variable) · 2
Derivative test → After, If

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Important terminology

function point derivative test local displaystyle maximum minimum increasing derivatives decreasing points calculus positive critical value inflection determine interval isbn

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
concavityinstance ofIn conjunction with other information0.80text
inflection pointsinstance ofIn conjunction with other information0.80text
and asymptotesinstance ofIn conjunction with other information0.80text
it can be used to sketch the graph of a functioninstance ofIn conjunction with other information0.80text
Derivative testhas applicationThe0.60section
Derivative testhas applicationIn0.60section
Derivative testrelated to ExampleSay0.60section
Derivative testrelated to ExampleTo0.60section
Derivative testrelated to ExampleAs0.60section
Derivative testrelated to ExampleThus0.60section
Derivative testrelated to External linksSecond Derivative Test0.60section
Derivative testrelated to External linksMathworldConcavity0.60section

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