mean-value theorem
Let be a function which is continuous on the interval and differentiable on . Then there exists a number such that
(1) |
The geometrical meaning of this theorem is illustrated in the picture:
The dashed line connects the points and . There is between and at which the tangent to has the same slope as the dashed line.
The mean-value theorem is often used in the integral context: There is a such that
(2) |
Title | mean-value theorem |
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Canonical name | MeanvalueTheorem |
Date of creation | 2013-03-22 12:20:39 |
Last modified on | 2013-03-22 12:20:39 |
Owner | mathwizard (128) |
Last modified by | mathwizard (128) |
Numerical id | 9 |
Author | mathwizard (128) |
Entry type | Theorem |
Classification | msc 26A06 |
Related topic | RollesTheorem |
Related topic | IntermediateValueTheorem |
Related topic | ExtendedMeanValueTheorem |
Related topic | ProofOfExtendedMeanValueTheorem |
Related topic | DerivationOfWaveEquation |