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