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love4math
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Help Please! Studying for test : Lagrange Multipliers!
Good morning all. I am having trouble with the next step to the following problem:
Q.Find all realtive extrema of x^2y^2 subject to the constraint 4x^2 + y^2 = 8.
g(x)= x^2y^2 f(x) = 4x^2 + y^2 = 8.
the gradiant of f = <8x,2y>
the gradiant of g = <2xy^2, 2x^2y>
therefore..
2xy^2 + 2x^2y = lamda (8x+2y)
lamda(8x) = 2xy^2 & lamda(2y)= 2x^2y
lamda = 2xy^2/8x & lamda = 2x^2y/2y
2x^2y/8x = 2xy^2/2y
4x^2 = y^2
I'm confused about how to find the extremas.
Can anyone help me?
Thanks all
Good morning all. I am having trouble with the next step to the following problem:
Q.Find all realtive extrema of x^2y^2 subject to the constraint 4x^2 + y^2 = 8.
g(x)= x^2y^2 f(x) = 4x^2 + y^2 = 8.
the gradiant of f = <8x,2y>
the gradiant of g = <2xy^2, 2x^2y>
therefore..
2xy^2 + 2x^2y = lamda (8x+2y)
lamda(8x) = 2xy^2 & lamda(2y)= 2x^2y
lamda = 2xy^2/8x & lamda = 2x^2y/2y
2x^2y/8x = 2xy^2/2y
4x^2 = y^2
I'm confused about how to find the extremas.
Can anyone help me?
Thanks all