Statements (16)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
Continuous functions
Differentiable functions |
| gptkbp:field |
gptkb:Calculus
|
| gptkbp:generalizes |
gptkb:Rolle's_theorem
gptkb:Lagrange's_mean_value_theorem |
| https://www.w3.org/2000/01/rdf-schema#label |
Cauchy's mean value theorem
|
| gptkbp:namedAfter |
gptkb:Augustin-Louis_Cauchy
|
| gptkbp:publicationYear |
1821
|
| gptkbp:publishedIn |
gptkb:Cours_d'Analyse
|
| gptkbp:relatedTo |
gptkb:Mean_value_theorem
|
| gptkbp:sentence |
If functions f and g are continuous on [a, b] and differentiable on (a, b), and g'(x) ≠ 0 for all x in (a, b), then there exists c in (a, b) such that (f(b)-f(a))/(g(b)-g(a)) = f'(c)/g'(c).
|
| gptkbp:statedIn |
Real analysis
|
| gptkbp:usedIn |
Proof of L'Hôpital's rule
|
| gptkbp:bfsParent |
gptkb:L'Hôpital's_rule_(mathematics)
|
| gptkbp:bfsLayer |
6
|