find the extremea of f(x,y) = x^2 -4y^2 subject to g(x,y) = x^2+ 4xy +6y^2 =2o.
making use of lagrange multiplier, i got
f(x,y) has a min or max when x^2 +5xy+4y^2 = o and that it has to also fulfil the conditions of g(x,y) = x^2+ 4xy +6y^2 =2o right?
when i solve these 2 equations via simultaneous, i got y=0 and x=2y. then how do i solve the last part?
subbing x into x^2+ 4xy +6y^2 =2o , i got 10y^4 -172y^2 +400=0.
so y^2 = (172 + (29544)^(1/2) )/ 20 or y^2 = (172 - (29544)^(1/2) )/ 20
then how do i get an equation in terms of just y alone and not y^2?
from here, what do i sub into x and y to find the points where f has a local minima and maxima?
thanks!