Function Expression :
\[f(x)=\sqrt{2x+1}+2\sqrt{4-x} \]Domain
\[\left[- \frac{1}{2}, 4\right] \]Limits
\[\lim_{x \overset{>}{\rightarrow- \frac{1}{2}} }f(x) = 3 \sqrt{2} \]\[\lim_{x \overset{<}{\rightarrow4} }f(x) = 3 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{1}{\sqrt{2 x + 1}} - \frac{1}{\sqrt{4 - x}} \]\[f^{\,\prime}(x)=\frac{1}{\sqrt{2 x + 1}} - \frac{1}{\sqrt{4 - x}} \]
\[f^{\,\prime}(x)=\frac{\sqrt{4 - x} - \sqrt{2 x + 1}}{\sqrt{4 - x} \sqrt{2 x + 1}} \]
Integral
\[F(x) = - \frac{4 \left(4 - x\right)^{\frac{3}{2}}}{3} + \frac{\left(2 x + 1\right)^{\frac{3}{2}}}{3} \]Sign Table
Variation Table
Plot
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