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$\large f\left( x \right) =\sqrt { 21+4x-{ x }^{ 2 } } -\sqrt { 10+3x-{ x }^{ 2 } }$

If the maximum value of the function given above occurs at $x={ x }_{ 0 }$ and the maximum value is ${y }_{ 0 }$, find ${ x }_{ 0 }+{ y }_{ 0 }$.

Inspiration.

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