Find the range of the function `f(x)=2sqrt(x-2)+sqrt(4-x)`

Explanation

Clearly domain of the function is [2,4] Now ,
`f(x) =(1)/sqrt(x-2)-(1)/2sqrt(4-x)`
f(x)=0
or `sqrt(x-2)=2sqrt(4-x)`
or x-2=16-4x
or `x=(18)/(5)`
Now f(2)=`sqrt(2),f(18/5)=2sqrt(18)/(5)-2+sqrt(4-(18)/(5)=sqrt(10)`
f(4)=`2sqrt(2)`
Hence range of the function is `sqrt(2),sqrt(10)`
Also here `x=(18//5)` is the point of global maxima.