# JEE Main & Advanced Mathematics Applications of Derivatives Rolle's Theorem

## Rolle's Theorem

Category : JEE Main & Advanced

If $f(x)$is such that,

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

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

(iii) $f(a)=f(b)$

Then there exists at least one value $'c'$ of $x$ in the open interval $(a,\,\,b)$ such that $f'(c)=0$.

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