Function Expression :
\[f(x)=1-(x^2+3x+1 )e^x \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 1 \]\[\lim_{x \rightarrow+\infty}f(x) = -\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\left(- 2 x - 3\right) e^{x} + \left(- x^{2} - 3 x - 1\right) e^{x} \]\[f^{\,\prime}(x)=\left(- x^{2} - 5 x - 4\right) e^{x} \]
\[ \]
Integral
\[F(x) = x + \left(- x^{2} - x\right) e^{x} \]Sign Table
Variation Table
Plot
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