Problem :
Find the range of the function: $f(x) = \sqrt{x-1}+2\sqrt{3-x}$
Solution :
Domain of this function can be determined as :
$x - 1 >0 ; 3-x >0 \Rightarrow x >0 ; x <3 ;$
$\therefore $ domain of $x \in [1,3]$
Now if I put the values of this domain in my function then it gives the following values :
at 1 ; the value of the function is $2\sqrt{2}$
at 2 : the value of the function is $ 1+2 = 3$
at 3 : the value of the function is $2$
Can we say that the maximum value of the function is 3 and minimum value of the function is 2;
Therefore the range of this function is [2,3] but this answer is wrong. please suggest..
Also suggest that how can we use differentiation method to find the range... thanks.