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