Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
Real-valued functions
Continuous functions Differentiable functions |
| gptkbp:category |
gptkb:Mathematical_analysis
Theorems in calculus |
| gptkbp:field |
gptkb:Calculus
|
| gptkbp:formedBy |
gptkb:Michel_Rolle
1691 |
| gptkbp:hasSpecialCase |
gptkb:Mean_Value_Theorem
|
| https://www.w3.org/2000/01/rdf-schema#label |
Rolle's Theorem
|
| gptkbp:namedAfter |
gptkb:Michel_Rolle
|
| gptkbp:prerequisite |
Continuity
Differentiability Real analysis |
| gptkbp:relatedTo |
gptkb:Intermediate_Value_Theorem
gptkb:Mean_Value_Theorem Fermat's Theorem (stationary points) |
| gptkbp:state |
If a real-valued function is continuous on [a, b], differentiable on (a, b), and f(a) = f(b), then there exists c in (a, b) such that f'(c) = 0.
|
| gptkbp:usedIn |
Proof of Mean Value Theorem
|
| gptkbp:bfsParent |
gptkb:Mean_Value_Theorem
|
| gptkbp:bfsLayer |
7
|