Home/Differential Calculus/Rolle's theorem/Formula7.1. Rolle's theoremFormulaIn 7.1. Rolle's theoremFormulaCopy LaTeXf is continuous at [a,b], f is differentiable at (a,b), f(a)=f(b)⇒∃c∈(a,b):f′(c)=0f\text{ is continuous at }[a,b],\ f\text{ is differentiable at }(a,b),\ f(a)=f(b) \Rightarrow \exists c\in(a,b): f'(c)=0f is continuous at [a,b], f is differentiable at (a,b), f(a)=f(b)⇒∃c∈(a,b):f′(c)=0TagsDifferential calculusContinuityDerivativeTheoremRolle's theoremExplore the ideaExplore the ideaVariablesaaaPoint or real constantbbbInterval endpoint or constantcccIntermediate point (MVT, Rolle)fffFunctionf′f'f′Derivative of fffRelated topicsMean value theoremFound an error? Contact us.Related formulasRelatedFormulaf is continuous at [a,b], f is differentiable at (a,b)⇒∃c∈(a,b):f′(c)=f(b)−f(a)b−af\text{ is continuous at }[a,b],\ f\text{ is differentiable at }(a,b) \Rightarrow \exists c\in(a,b): f'(c)=\frac{f(b)-f(a)}{b-a}f is continuous at [a,b], f is differentiable at (a,b)⇒∃c∈(a,b):f′(c)=b−af(b)−f(a)Open formulaOpen in section