Question

Use the technique of Lagrange Multipliers to find the maximum vlaue of the function f(x,y)=xy+y given that 9x^2 + 10y^4 = 9

Answer 1

where are you stuck?

Answer 2

I dont know how to do the problem

Answer 3

Could you show me?

Answer 4

hihihi, it's hard, I am working on it, still not get a beautiful result. I am sorry for big mouth in previous post. XD

Answer 5

can you write down the equation with the lagrange constraint ?

Answer 6

I dont really know what that means

Answer 7

I dont know how to do that

Answer 8

Paul's online notes are helpful
http://tutorial.math.lamar.edu/Classes/CalcIII/LagrangeMultipliers.aspx

meanwhile, you define a new function
g(x,y,L)= f(x,y) + L*constraint
(by convention, the multiplier is designated as a Greek lambda, but L is easier to type)

Answer 9

in this case
g(x,y,L) = xy + y + L(9x^2 + 10y^4 - 9)

can you find the partial derivatives with respect to x, y and L ?

Answer 10

yes for x and y but how would I do L?

Answer 11

you are working with g(x,y,L)
\[ g_L = 9x^2 + 10y^4 - 9 \]

Answer 12

L is a variable, and you treat it the same as you treat x and y
in the function g(x,y,L)

Answer 13

okay so its 18x-40y^3 right?