Statements (20)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
continuous functions
real-valued functions |
| gptkbp:category |
theorems in calculus
theorems in real analysis |
| gptkbp:field |
gptkb:mathematics
calculus real analysis |
| gptkbp:firstPublished |
19th century
|
| https://www.w3.org/2000/01/rdf-schema#label |
Intermediate value theorem
|
| gptkbp:implies |
a continuous function on [a, b] attains every value between f(a) and f(b)
|
| gptkbp:namedAfter |
intermediate value
|
| gptkbp:relatedTo |
gptkb:Mean_value_theorem
gptkb:Extreme_value_theorem gptkb:Bolzano's_theorem |
| gptkbp:sentence |
If a function f is continuous on a closed interval [a, b], and d is any value between f(a) and f(b), then there exists at least one c in [a, b] such that f(c) = d.
|
| gptkbp:usedIn |
analysis of continuous functions
proofs of root existence |
| gptkbp:bfsParent |
gptkb:Poincaré–Miranda_theorem
|
| gptkbp:bfsLayer |
6
|