8. The maximum value of the function $f(x)=\sqrt{x^{4}-3 x^{2}-6 x+13}-\sqrt{x^{1}-x^{2}+1}$ is

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8. $\sqrt{10}$ Hint: $f(x)=\sqrt{(x-3)^{2}+\left(x^{2}-2\right)^{2}}-\sqrt{(x-0)^{2}+\left(x^{2}-1\right)^{2}}$ The geometric meaning is the maximum value of the difference in distances from a point $P\left(x, x^{2}\right)$ on the parabola $y=x^{2}$ to points $A(3,2)$ and $B(0,1)$. By ||$P A|-| P B||$ $\leqslant|A B|$, we know that when $P$ is at the extension of $A B$ at point $P_{0}$, $f(x)$ has its maximum value.