# JEE Main & Advanced Mathematics Applications of Derivatives Lagrange's Mean Value Theorem

## Lagrange's Mean Value Theorem

Category : JEE Main & Advanced

If a function $f(x)$ is such that,

(i) It is continuous in the closed interval $[a,b]$

(ii) It is derivable in the open interval $(a,\,b)$

Then there exists at least one value $'c'$ of $x$ in the open interval $(a,b)$ such that $\frac{f(b)-f(a)}{b-a}=f'(c)$.

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