Statements (14)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
real-valued functions
|
| gptkbp:category |
theorems in calculus
|
| gptkbp:field |
calculus
|
| gptkbp:firstPublished |
1691
|
| https://www.w3.org/2000/01/rdf-schema#label |
Roll's theorem
|
| gptkbp:namedAfter |
gptkb:Michel_Rolle
|
| gptkbp:requires |
function must be continuous on closed interval
function must be differentiable on open interval function values at endpoints must be equal |
| gptkbp:sentence |
If a 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 the mean value theorem
|
| gptkbp:bfsParent |
gptkb:Richard_Roll
|
| gptkbp:bfsLayer |
7
|