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