Function Expression :
\[f(x)=\frac{6}{\frac{1}{x+3}+4} \]Domain
\[\left]-\infty, - \frac{13}{4}\right[ \cup \left]- \frac{13}{4}, -3\right[ \cup \left]-3, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = \frac{3}{2} \]\[\lim_{x \overset{<}{\rightarrow- \frac{13}{4}} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow- \frac{13}{4}} }f(x) = -\infty \]
\[\lim_{x \overset{<}{\rightarrow-3} }f(x) = 0 \]
\[\lim_{x \overset{>}{\rightarrow-3} }f(x) = 0 \]
\[\lim_{x \rightarrow+\infty}f(x) = \frac{3}{2} \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{6}{\left(4 + 1 \cdot \frac{1}{x + 3}\right)^{2} \left(x + 3\right)^{2}} \]\[f^{\,\prime}(x)=\frac{6}{\left(4 x + 13\right)^{2}} \]
\[ \]
Integral
\[F(x) = \frac{3 x}{2} - \frac{3 \log{\left(4 x + 13 \right)}}{8} \]Sign Table
Variation Table
Plot
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