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