Five, find the maximum and minimum values of the function $y=\arcsin \frac{x}{2}+\sqrt{4-x^{2}}$ on its domain.
Five, solve. The domain of the function is $[-2,2]$.
$$
\begin{aligned}
y^{\prime} & =\frac{1-x}{\sqrt{4-x^{2}}}, \text { let } y^{\prime}=0 \text { to get the critical point } x=1 . \\
\left.\because \quad y\right|_{x=1} & =\frac{\pi}{6}+\sqrt{3}, y=-\frac{\pi}{2}, \\
y=2 & =\frac{\pi}{2}, \\
\therefore \quad y_{m} y_{x} & =\frac{\pi}{6}+\sqrt{3}, y_{m i n}=-\frac{\pi}{2} .
\end{aligned}
$$