Prove that there is no differentiable function $\displaystyle f:[-1,1] \to \mathbb {R}$ such that $\displaystyle f'(x)=[x]$

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- Jan 9th 2010, 07:36 AMflower3no differentiable function
Prove that there is no differentiable function $\displaystyle f:[-1,1] \to \mathbb {R}$ such that $\displaystyle f'(x)=[x]$

- Jan 9th 2010, 07:42 AMShanks
Hint:Applying Darboux's theorem! If the statement is true, then it leads to cantradiction to Darboux's theorem.