Answer:
Absolute minimum = 1.414
Absolute maximum = 2.828
Step-by-step explanation:
[tex]g(x,y)=\sqrt {x^2+y^2} \ constraints: 1\leq x\leq 2 ,\ 1\leq y\leq2[/tex]
For absolute minimum we take the minimum values of [tex]x[/tex] and [tex]y[/tex].
[tex]x_{minimum} =1\\y_{minimum}=1\\[/tex]
Plugging in the minimum values in the function.
[tex]g(1,1)=\sqrt {1^2+1^2}\\g(1,1) = \sqrt{1+1}\\g(1,1)=\sqrt {2}\\g(1,1)=\pm 1.414\\[/tex]
Absolute minimum value will be always positive.
∴ Absolute minimum = 1.414
For absolute maximum we take the maximum values of [tex]x[/tex] and [tex]y[/tex].
[tex]x_{maximum} =2\\y_{maximum}=2\\[/tex]
Plugging in the maximum values in the function.
[tex]g(2,2)=\sqrt {2^2+2^2}\\g(2,2) = \sqrt{4+4}\\g(2,2)=\sqrt {8}\\g(2,2)=\pm 2.828\\[/tex]
Absolute maximum value will be always positive.
∴ Absolute maximum = 2.828
