MathLiveMean value theorem
For a continuous function on a closed interval that is differentiable inside it, there is some point where the instantaneous slope equals the slope of the secant joining the endpoints. It is used to relate a function's values to its derivative.
\exists c \in (a, b) : f(b) - f(a) = (b - a) f'(c)What the symbols mean
| a continuous function on $[a,b]$ that is differentiable on $(a,b)$ | |
| left endpoint of the interval | |
| right endpoint of the interval | |
| a point strictly between $a$ and $b$ where the tangent is parallel to the secant | |
| derivative of $f$ at $c$ |
About this formula
- FieldMathematics
- TopicDifferential calculus
- LevelUniversity
- Also calledLagrange's mean value theorem, law of the mean, MVT, tangent parallel to secant, existence of tangent parallel to chord, average rate of change equals instantaneous rate
- SourceWikidata Q189136
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