Function Expression :
\[f(x)=2(x-2 )\sqrt{x}-x \]Domain
\[\left[0, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = 0 \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=2 \sqrt{x} - 1 + \frac{2 x - 4}{2 \sqrt{x}} \]\[f^{\,\prime}(x)=\frac{- \sqrt{x} + 3 x - 2}{\sqrt{x}} \]
\[ \]
Integral
\[F(x) = \frac{4 \sqrt{x} \left(x - 2\right)^{2}}{5} + \frac{8 \sqrt{x} \left(x - 2\right)}{15} - \frac{32 \sqrt{x}}{15} - \frac{x^{2}}{2} \]Sign Table
Variation Table
Plot
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