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