What are some wide rangle of applications of mean value theorem

Mean value theorem comes in differentiation.

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  • Mean value theorem as such is nt used alone widely, but it is used a mathematical tool to solve problems. It basically serves as a tool for solving other problems which are otherwise related to the real world.
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  • Some more applications: If the derivative of a function f is everywhere strictly positive, then f is a strictly increasing function. Suppose f is differentiable on whole of R, and f′(x) is a constant. Then f is linear. Mean Value theorem plays an important role in the proof of Fundamental Theorem of Calculus.
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