Function Expression :
\[f(x)=\frac{6}{\sqrt{4x+5}} \]Domain
\[\left]- \frac{5}{4}, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow- \frac{5}{4}} }f(x) = +\infty \]\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{12}{\left(4 x + 5\right)^{\frac{3}{2}}} \]\[f^{\,\prime}(x)=- \frac{12}{\left(4 x + 5\right)^{\frac{3}{2}}} \]
\[ \]
Integral
\[F(x) = 6 \left(\begin{cases} 0 & \text{for}\: \frac{1}{\left|{x + \frac{5}{4}}\right|} < 1 \wedge \left|{x + \frac{5}{4}}\right| < 1 \\\sqrt{x + \frac{5}{4}} & \text{for}\: \frac{1}{\left|{x + \frac{5}{4}}\right|} < 1 \vee \left|{x + \frac{5}{4}}\right| < 1 \\\frac{{G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & \frac{3}{2} \\\frac{1}{2} & 0 \end{matrix} \middle| {x + \frac{5}{4}} \right)}}{2} + \frac{{G_{2, 2}^{0, 2}\left(\begin{matrix} \frac{3}{2}, 1 & \\ & \frac{1}{2}, 0 \end{matrix} \middle| {x + \frac{5}{4}} \right)}}{2} & \text{otherwise} \end{cases}\right) \]Sign Table
Variation Table
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