- #1
pbialos
I have an exercise i would really appreciate if you could help me with:
Given f:R^2->R, f(x,y)=x^4+y^4-2(x-y)^2
1-Prove that (sqrt(2),-sqrt(2)) and (-sqrt(2),sqrt(2)) are absolute minimums
2-are there any local maximums?
1-I found out that the critical points lie on the line y=-x, and i suppose i should prove that f(sqrt(2),-sqrt(2))=-8<f(x,y) for every (x,y) but i don't know how to do this.
2-I found that there arent any local maximums, but i would like you to correct me if i am wrong.
Thank you very much, Paul.
Given f:R^2->R, f(x,y)=x^4+y^4-2(x-y)^2
1-Prove that (sqrt(2),-sqrt(2)) and (-sqrt(2),sqrt(2)) are absolute minimums
2-are there any local maximums?
1-I found out that the critical points lie on the line y=-x, and i suppose i should prove that f(sqrt(2),-sqrt(2))=-8<f(x,y) for every (x,y) but i don't know how to do this.
2-I found that there arent any local maximums, but i would like you to correct me if i am wrong.
Thank you very much, Paul.