538. Investigate the behavior of the function $f(x)=3+\sqrt{x}$ at the point $x=4$.
Solution. Let's find the derivative; $f^{\prime}(x)=\frac{1}{2 \sqrt{x}}$ Calculate the value of the derivative at $x=4: f^{\prime}(4)=\frac{1}{2 \sqrt{4}}=\frac{1}{4}>0$. From this, we conclude that the given function is increasing at the point $x=4$.