Function Expression :
\[f(x)=(1-x )e^{-x}-x-2 \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = +\infty \]\[\lim_{x \rightarrow+\infty}f(x) = -\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \left(1 - x\right) e^{- x} - 1 - e^{- x} \]\[f^{\,\prime}(x)=\left(x - e^{x} - 2\right) e^{- x} \]
\[ \]
Integral
\[F(x) = - \frac{x^{2}}{2} - 2 x + x e^{- x} \]Sign Table
Variation Table
Plot
Elapsed Time: 0.0124 seconds