Factor 2x^2 + y^2 + 2z^2 + 2xy + 2yz + 2xz + x - 3z

W

wickeddude12

New member
Joined
Oct 17, 2008
Messages
13
Factor 2x^2 + y^2 + 2z^2 + 2xy + 2yz + 2xz + x - 3z

________________________
Edited by stapel -- Reason for edit: Replacing picture of text with text.
 
Re: Factor

wickeddude12 said:
[attachment=0:1l3q5gvr]eqn.gif[/attachment:1l3q5gvr]
Click to expand...

This is a wicked one - I have to think about a bit!!!
 
Re: Factor

I'm not sure it is even factorable. However, I am supposed to determine whether this function has a global minimum at (x,y,z)=(-1/2,-1,3/2). I already know it is a local minimum since the partial derivatives are all zero (this goes into calculus though).
 
Hi Wickeddude,

If the function z = f(x,y) you refer to is the one implicitly given by 2x^2 + y^2 + 2z^2 + 2xy + 2yz + 2xz + x - 3z = 0, notice that this is an upward-facing quadratic in z.
 
2z^2 + z(2x + 2y - 3) + x = 0

That's a quadratic in 'z'.

Now if you make section at constant 'x' (or constant 'y') - you would get a parabola on z-y plane (or z-x plane).
 
You must log in or register to reply here.
Top