Function Expression :
\[f(x)=-\frac{1}{4}xe^{-\frac{x}{2}}+1 \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = +\infty \]\[\lim_{x \rightarrow+\infty}f(x) = 1 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{x e^{- \frac{x}{2}}}{8} - \frac{e^{- \frac{x}{2}}}{4} \]\[f^{\,\prime}(x)=\frac{\left(x - 2\right) e^{- \frac{x}{2}}}{8} \]
\[ \]
Integral
\[F(x) = x + \frac{\left(x + 2\right) e^{- \frac{x}{2}}}{2} \]Sign Table
Variation Table
Plot
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