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that there exists a linear transformation $T∈L(\mathbb{R}^n;\mathbb{R}^m)$ such that $Df(x)=T$ for all $ x∈V$. Prove

that there is a $ c∈\mathbb{R}^m$ such that $f(x)=c+T(x)$ for all $ x∈V$.

(I found $Df(x)=DT=T$, is that correct and what this means?)