NEW FUNCTION

Function Expression :

\[f(x)=3+(x-1 )e^{-x} \]

Domain

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

Limits

\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 3 \]
\[ \]

Derivate

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

Integral

\[F(x) = 3 x - x e^{- x} \]

Sign Table

Variation Table

Plot

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