NEW FUNCTION

Function Expression :

\[f(x)=(1-x )e^{-x}+1 \]

Domain

\[]-\infty ;+\infty [ \]

Limits

\[\lim_{x \rightarrow-\infty}f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 1 \]
\[ \]

Derivate

\[f^{\,\prime}(x)=- \left(1 - x\right) e^{- x} - e^{- x} \]
\[f^{\,\prime}(x)=\left(x - 2\right) e^{- x} \]
\[ \]

Integral

\[F(x) = x + x e^{- x} \]

Sign Table

Variation Table

Plot

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