MHB Finding Critical Points and Extrema for g(x, y) = sqrt{x^2 + y^2 + 1}

[harpazo]

Find the critical points and extrema of the function

g (x, y) = sqrt {x^2 + y^2 + 1}. Can someone get me started here? I also would like the solution steps. I said solution steps not the solution.

Do it like this:

Step 1...

Step 2...

Step 3...etc...

 

[Prove It]

Find the critical points and extrema of the function

g (x, y) = sqrt {x^2 + y^2 + 1}. Can someone get me started here? I also would like the solution steps. I said solution steps not the solution.

Do it like this:

Step 1...

Step 2...

Step 3...etc...

Sigh.

First of all, a "solution" is NOT the final answer, as you are implying here. A solution IS all the steps involved. And you won't get them here, as it is expected that students attempt their problems first, show where they have gotten stuck, and then get some guidance on how to proceed. In short, YOU will be doing your work, not us.

As for getting started, have you at least done a sketch of your region? That might at least give you a ball park estimate of where the extrema might be...