Function Expression :
\[f(x)=-(x+1 )^2. e^{-x} \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\left(- 2 x - 2\right) e^{- x} + \left(x + 1\right)^{2} e^{- x} \]\[f^{\,\prime}(x)=\left(x^{2} - 1\right) e^{- x} \]
\[ \]
Integral
\[F(x) = \left(x^{2} + 4 x + 5\right) e^{- x} \]Sign Table
Variation Table
Plot
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