Function Expression :
\[f(x)=1-2(x^2-x )e^{2x} \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 1 \]\[\lim_{x \rightarrow+\infty}f(x) = -\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\left(2 - 4 x\right) e^{2 x} + 2 \left(- 2 x^{2} + 2 x\right) e^{2 x} \]\[f^{\,\prime}(x)=\left(2 - 4 x^{2}\right) e^{2 x} \]
\[f^{\,\prime}(x)=2 \cdot \left(1 - 2 x^{2}\right) e^{2 x} \]
Integral
\[F(x) = x + \left(- x^{2} + 2 x - 1\right) e^{2 x} \]Sign Table
Variation Table
Plot
Elapsed Time: 0.0033 seconds