NEW FUNCTION

Function Expression :

\[f(x)=4e^x-e^{2x}+2-2x \]

Domain

\[]-\infty ;+\infty [ \]

Limits

\[\lim_{x \rightarrow-\infty}f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = -\infty \]
\[ \]

Derivate

\[f^{\,\prime}(x)=- 2 e^{2 x} + 4 e^{x} - 2 \]
\[f^{\,\prime}(x)=2 \left(- e^{2 x} + 2 e^{x} - 1\right) \]

Integral

\[F(x) = - x^{2} + 2 x - \frac{e^{2 x}}{2} + 4 e^{x} \]

Sign Table

Variation Table

Plot

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