Find the maximum value of
\[f(x) = \sqrt{8x - x^2} - \sqrt{14x - x^2 - 48}.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the maximum value of
\[f(x) = \sqrt{8x - x^2} - \sqrt{14x - x^2 - 48}.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
2 \sqrt{3}
Find the maximum value of
\[f(x) = \sqrt{8x - x^2} - \sqrt{14x - x^2 - 48}.\]
train