Mean value theorem
Teorema del valor medio
- Date
- 1691-1823 · confidence medium
- Place
- Paris, France
- Credited to
- Augustin-Louis Cauchy (general form, 1823); preceded by Michel Rolle (restricted case, 1691)
- Field
- Knowledge & symbols
What was discovered
For a differentiable function on an interval there is a point where the instantaneous slope equals the interval's average slope. Cauchy gives it its modern general form in 1823, after Rolle's 1691 case restricted to polynomials.
Indian mathematician Parameshvara (15th c.) had already described a special case for inverse interpolation of the sine.
What it led to
- Rigorous 19th-century mathematical analysis
- Proofs of L'Hôpital's rule and Taylor's theorem
- Foundation for error and approximation calculus