Find absolute extrema of f(x,y)= x^2+2xy+y^2, bound by |x|

Question

Find absolute extrema of f(x,y)= x^2+2xy+y^2, bound by |x|<=2, |y|<=1 Find absolute extrema of f(x,y)= x^2+2xy+y^2, bound by |x|<=2, |y|<=1 @Mathematics

anonymous · Answer

now i got the maximum by putting my lines x=-2,2 and y=-1,1 however when i try to find the functions zeroes i get x=-y... am i supposed to put that into the equation and evaluate so....  x^2+2(-y)y+y^2=x^2?

anonymous · Answer

and they get (x,-x,0) as an absolute minima

anonymous · Answer

just wondering if i did right in which the function x^2 will always be positive... and what would happen if i got something that didn't exactly get 0?

anonymous · Answer

Is this Calculus 2?  I am doing single variable versions of this in Calculus 1 this week, too.

anonymous · Answer

this is calculus 3... calculus two is more into surface area and integrals... calc 3 is multivariable

anonymous · Answer

Right on. Bye the way, I thought you did great work helping that fellow rationalize the denom.  Good teaching!

anonymous · Answer

thanks