Function Expression :
\[f(x)=(2x+3 )e^{-x}+x-1 \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \left(2 x + 3\right) e^{- x} + 1 + 2 e^{- x} \]\[f^{\,\prime}(x)=\left(- 2 x + e^{x} - 1\right) e^{- x} \]
\[ \]
Integral
\[F(x) = \frac{x^{2}}{2} - x + \left(- 2 x - 5\right) e^{- x} \]Sign Table
Variation Table
Plot
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