Checking Optimal Points of f(x,y,z)=3+4(x^2)+2(y^2)+6(z^2)-4xy+2yz+4xz

[mlb123]

So, I have a function f(x,y,z) and need to show if (0,0,0) is an optimal point. If it is, I have to determine local max and min.

f(x,y,z)=3+4(x^2)+2(y^2)+6(z^2)-4xy+2yz+4xz


I've been stuck on this all day to no avail. I know that the idea is to get it into a form such that it'll be 3+(___)^2+(___)^2+(___)^2 or 3-(___)^2-(___)^2-(___)^2 to find if it's a local min or max, but I'm just really stuck here. Any help would be appreciated.

 

[Deleted member 4993]

So, I have a function f(x,y,z) and need to show if (0,0,0) is an optimal point. If it is, I have to determine local max and min.

f(x,y,z)=3+4(x^2)+2(y^2)+6(z^2)-4xy+2yz+4xz


I've been stuck on this all day to no avail. I know that the idea is to get it into a form such that it'll be 3+(___)^2+(___)^2+(___)^2 or 3-(___)^2-(___)^2-(___)^2 to find if it's a local min or max, but I'm just really stuck here. Any help would be appreciated.

What is the definition of optimal point of a function?

 

[stapel]

I have a function f(x, y, z) = 3 + 4x² + 2y² + 6z² - 4xy + 2yz + 4xz, and need to show if (0, 0, 0) is an optimal point. If it is, I have to determine local max and min....

I know that the idea is to get it into a form such that it'll be 3+(___)^2+(___)^2+(___)^2 or 3-(___)^2-(___)^2-(___)^2...

How do you "know" this? Thank you!