Function Expression :
\[f(x)=(x+0.5 ). e^{(-2x )} \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- 2 \left(x + \frac{1}{2}\right) e^{- 2 x} + e^{\left(-1\right) 2 x} \]\[f^{\,\prime}(x)=- 2 x e^{- 2 x} \]
\[ \]
Integral
\[F(x) = \frac{\left(- x - 1\right) e^{- 2 x}}{2} \]Sign Table
Variation Table
Plot
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