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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

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# Homework Help: Help Please! Studying for test : Lagrange Multipliers

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