6. If the function $y=3 \sin x-4 \cos x$ attains its maximum value at $x_{0}$, then the value of $\tan x_{0}$ is $\qquad$
Solve
$y=5\left(\frac{3}{5} \sin x-\frac{4}{5} \cos x\right)=5 \sin (x-\varphi)$, when $y$ reaches its maximum value,
$$
x_{0}-\varphi=\frac{\pi}{2} \Rightarrow \sin x_{0}=\cos \varphi=\frac{3}{5}, \cos x_{0}=-\sin \varphi=-\frac{4}{5} \Rightarrow \tan x_{0}=-\frac{3}{4}
$$