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Mean-Value Theorem

Let f(x) be differentiable on the open interval (a,b) and continuous on the closed interval [a,b]. Then there is at least one point c in (a,b) such that

f^'(c)=(f(b)-f(a))/(b-a).

The theorem can be generalized to extended mean-value theorem.

See also

Extended Mean-Value Theorem, Gauss's Mean-Value Theorem, Intermediate Value Theorem Explore this topic in the MathWorld classroom

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References

Anton, H. Calculus with Analytic Geometry, 2nd ed. New York: Wiley, pp. 262-263, 1984.Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, pp. 1097-1098, 2000.Jeffreys, H. and Jeffreys, B. S. "Mean-Value Theorems." §1.13 in Methods of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University Press, pp. 49-50, 1988.

Cite this as:

Weisstein, Eric W. "Mean-Value Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Mean-ValueTheorem.html

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