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