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Question Number 56205 by 121194 last updated on 12/Mar/19

$$\mathrm{find}\left(\mathrm{or}\mathrm{prove}\mathrm{it}{\mathrm{can}}^{\prime }\mathrm{t}\mathrm{exist}\right)\mathrm{a}f:\mathbb{R}\to \mathbb{R}\mathrm{diferentiable}$$ $$\mathrm{such}\mathrm{that}$$ $$\underset{a-\delta }{\stackrel{a+\delta }{\int }}f\left(x\right)dx=0,\mathrm{\forall }a\in \mathbb{R},\delta >0$$ $$\frac{df}{dx}=0,\mathrm{\forall }x\in \mathbb{R}$$

Answered by MJS last updated on 12/Mar/19

$$f\left(x\right)=0$$

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