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