Function Expression :
\[f(x)=-x+1+\frac{(x-1 )}{e^x} \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = -\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \left(x - 1\right) e^{- x} - 1 + \frac{1}{e^{x}} \]\[f^{\,\prime}(x)=\left(- x - e^{x} + 2\right) e^{- x} \]
\[ \]
Integral
\[F(x) = - \frac{x^{2}}{2} + x - x e^{- x} \]Sign Table
Variation Table
Plot
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