Function Expression :
\[f(x)=\frac{6x}{\frac{1}{+3}+4x} \]Domain
\[\left]-\infty, - \frac{1}{12}\right[ \cup \left]- \frac{1}{12}, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = \frac{3}{2} \]\[\lim_{x \overset{<}{\rightarrow- \frac{1}{12}} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow- \frac{1}{12}} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = \frac{3}{2} \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{24 x}{\left(4 x + 1 \cdot \frac{1}{3}\right)^{2}} + \frac{6}{4 x + 1 \cdot \frac{1}{3}} \]\[f^{\,\prime}(x)=\frac{18}{\left(12 x + 1\right)^{2}} \]
\[ \]
Integral
\[F(x) = \frac{3 x}{2} - \frac{\log{\left(12 x + 1 \right)}}{8} \]Sign Table
Variation Table
Plot
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