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Rolle’s Theorem. |
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Answer» Rolle’s Theorem is a particular case of the mean value theorem which satisfies certain conditions. At the same time, Lagrange’s mean value theorem is the mean value theorem itself or the first mean value theorem. In general, one can understand mean as the average of the given values. But in the case of integrals, the process of finding the mean value of two different functions is different. Let us learn Rolle’s theorem and the mean value of such functions and their geometrical interpretation. Lagrange’s Mean Value Theorem If a function f is defined on the closed interval [a,b] satisfying the following conditions – i) The function f is continuous on the closed interval [a, b] ii)The function f is differentiable on the open interval (a, b) Then there exists a value x = c in such a way that f'(c) = [f(b) – f(a)]/(b-a) This theorem is also known as the first mean value theorem or Lagrange’s mean value theorem. |
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