Function Expression :
\[f(x)=(x+4 )e^{-\frac{1}{2}x} \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{\left(x + 4\right) e^{- \frac{x}{2}}}{2} + e^{\left(-1\right) 1 \cdot \frac{1}{2} x} \]\[f^{\,\prime}(x)=\frac{\left(- x - 2\right) e^{- \frac{x}{2}}}{2} \]
\[ \]
Integral
\[F(x) = \left(- 2 x - 12\right) e^{- \frac{x}{2}} \]Sign Table
Variation Table
Plot
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