10 . For real numbers $a, b$, we define the symbol $\max (a, b)$ as follows:
When $a^{3} b$, $\max (a, b)=a$; when $a<b$, $\max (a, b)=b$.

For example: $\max (3,-2)=3, \max (2,2)=2, \max (3,4)=4$. If the minimum value of the function $y=\max (x+4,-x+2)$ with respect to $x$ is $m$, then $\max (\sqrt{m}, m-1)=(\quad)$
(A) 1
(B) $\sqrt{2}$
(C) $\sqrt{3}$
(D) 2
Answer: (D)
Solution: When $x+4^{3}-x+2$, i.e., $x^{3}-1$,
$$
y=x+4^{3} 3,
$$

When $x+43,
$$

So $m=y_{\text {min }}=3, \max (\sqrt{m}, m-1)=\max (\sqrt{3}, 3-1)=2$. Therefore, the answer is (D).