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