Function Expression :
\[f(x)=\sqrt{5x-2}.4x^2 \]Domain
\[\left[\frac{2}{5}, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow\frac{2}{5}} }f(x) = 0 \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{10 x^{2}}{\sqrt{5 x - 2}} + 8 x \sqrt{5 x - 2} \]\[f^{\,\prime}(x)=\frac{2 x \left(25 x - 8\right)}{\sqrt{5 x - 2}} \]
\[ \]
Integral
\[F(x) = 4 \left(\begin{cases} \frac{2 x^{3} \sqrt{5 x - 2}}{7} - \frac{4 x^{2} \sqrt{5 x - 2}}{175} - \frac{32 x \sqrt{5 x - 2}}{2625} - \frac{128 \sqrt{5 x - 2}}{13125} & \text{for}\: \left|{x}\right| > \frac{2}{5} \\\frac{2 i x^{3} \sqrt{2 - 5 x}}{7} - \frac{4 i x^{2} \sqrt{2 - 5 x}}{175} - \frac{32 i x \sqrt{2 - 5 x}}{2625} - \frac{128 i \sqrt{2 - 5 x}}{13125} & \text{otherwise} \end{cases}\right) \]Sign Table
Variation Table
Plot
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