Home/Differential Calculus/Mean value theorem/Rolle's theoremSection 7.1Rolle's theoremFormulavizCopy 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)=0View detail →
FormulavizCopy 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)=0View detail →