Question

I get

x/(sqrt(x^2+y^2))
and
y/(sqrt(x^2+y^2))
If I then make them equal to zero I get x=0 and y=0, however now I am unsure about what to do.

Answer 1

Absolute minimum = 1.414

Absolute maximum = 2.828

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) = √(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) = √(4+4)\\g(2,2)=\sqrt {8}\\g(2,2)=\pm 2.828\\`

Absolute maximum value will be always positive.

∴ Absolute maximum = 2.828