Lagrange's Mean Value Theorem
GPTKB entity
Statements (17)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
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| gptkbp:alsoKnownAs |
gptkb:Mean_Value_Theorem
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| gptkbp:appliesTo |
Real-valued functions
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| gptkbp:field |
gptkb:Calculus
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| gptkbp:generalizes |
gptkb:Rolle's_Theorem
|
| https://www.w3.org/2000/01/rdf-schema#label |
Lagrange's Mean Value Theorem
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| gptkbp:namedAfter |
gptkb:Joseph-Louis_Lagrange
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| gptkbp:publishedIn |
18th century
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| gptkbp:requires |
Continuity on closed interval
Differentiability on open interval |
| gptkbp:state |
If a function is continuous on [a, b] and differentiable on (a, b), then there exists c in (a, b) such that f'(c) = (f(b) - f(a)) / (b - a)
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| gptkbp:usedIn |
Analysis
Estimation of function values Error analysis Proofs of Taylor's theorem |
| gptkbp:bfsParent |
gptkb:Mean_Value_Theorem
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| gptkbp:bfsLayer |
7
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