Function Expression :
\[f(x)=x-\frac{8}{3}+\frac{8}{e^x+2} \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=1 - \frac{8 e^{x}}{\left(e^{x} + 2\right)^{2}} \]\[f^{\,\prime}(x)=1 - \frac{8 e^{x}}{\left(e^{x} + 2\right)^{2}} \]
\[f^{\,\prime}(x)=\frac{\left(e^{x} + 2\right)^{2} - 8 e^{x}}{\left(e^{x} + 2\right)^{2}} \]
Integral
\[F(x) = \frac{x^{2}}{2} + \frac{4 x}{3} - 4 \log{\left(e^{x} + 2 \right)} \]Sign Table
Variation Table
Plot
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