Question

I get

Answer 1

Answer:

Absolute minimum = 1.414

Absolute maximum = 2.828

Step-by-step explanation:

$g(x,y)=\sqrt {x^2+y^2} \ constraints: 1\leq x\leq 2 ,\ 1\leq y\leq2$

For absolute minimum we take the minimum values of $x$ and $y$.

$x_{minimum} =1\\y_{minimum}=1$

Plugging in the minimum values in the function.

$g(1,1)=\sqrt {1^2+1^2}\\g(1,1) = \sqrt{1+1}\\g(1,1)=\sqrt {2}\\g(1,1)=\pm 1.414$

Absolute minimum value will be always positive.

∴ Absolute minimum = 1.414

For absolute maximum we take the maximum values of $x$ and $y$.

$x_{maximum} =2\\y_{maximum}=2$

Plugging in the maximum values in the function.

$g(2,2)=\sqrt {2^2+2^2}\\g(2,2) = \sqrt{4+4}\\g(2,2)=\sqrt {8}\\g(2,2)=\pm 2.828$

Absolute maximum value will be always positive.

∴ Absolute maximum = 2.828