Function Expression :
\[f(x)=\frac{x}{2}(1+\sqrt{x+4} ) \]Domain
\[\left[-4, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow-4} }f(x) = -2 \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{x}{4 \sqrt{x + 4}} + \frac{\sqrt{x + 4}}{2} + \frac{1}{2} \]\[f^{\,\prime}(x)=\frac{3 x + 2 \sqrt{x + 4} + 8}{4 \sqrt{x + 4}} \]
\[ \]
Integral
\[F(x) = - 2 x + \frac{\left(x + 4\right)^{\frac{5}{2}}}{5} - \frac{4 \left(x + 4\right)^{\frac{3}{2}}}{3} + \frac{\left(x + 4\right)^{2}}{4} - 8 \]Sign Table
Variation Table
Plot
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