Function Expression :
\[f(x)=\frac{x-3. x+6}{(x+3 )^2} \]Domain
\[\left]-\infty, -3\right[ \cup \left]-3, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 0 \]\[\lim_{x \overset{<}{\rightarrow-3} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow-3} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{\left(- 2 x - 6\right) \left(\left(-1\right) 3 x + x + 6\right)}{\left(x + 3\right)^{4}} - \frac{2}{\left(x + 3\right)^{2}} \]\[f^{\,\prime}(x)=\frac{2 \left(x - 9\right)}{\left(x + 3\right)^{3}} \]
\[ \]
Integral
\[F(x) = - 2 \log{\left(x + 3 \right)} - \frac{12}{x + 3} \]Sign Table
Variation Table
Plot
Elapsed Time: 0.1945 seconds