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