Function Expression :
\[f(x)=\frac{x^2}{2}(1+\sqrt{x+4} ) \]Domain
\[\left[-4, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow-4} }f(x) = 8 \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{x^{2}}{4 \sqrt{x + 4}} + x \left(\sqrt{x + 4} + 1\right) \]\[f^{\,\prime}(x)=\frac{x \left(5 x + 4 \sqrt{x + 4} + 16\right)}{4 \sqrt{x + 4}} \]
\[ \]
Integral
\[F(x) = \frac{x^{3}}{6} + \frac{\left(x + 4\right)^{\frac{7}{2}}}{7} - \frac{8 \left(x + 4\right)^{\frac{5}{2}}}{5} + \frac{16 \left(x + 4\right)^{\frac{3}{2}}}{3} \]Sign Table
Variation Table
Plot
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