GWR309
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f(x,y)=x^2y with the constraint of x^2+2y^2=6
Use lagrange multipliers to find the extrema.
Thanks!
Use lagrange multipliers to find the extrema.
Thanks!
Prove It said:Well, have you tried to solve the system
[math]\displaystyle \begin{align*} \nabla f(x, y) &= \lambda \nabla g(x, y) \\ g(x, y) &= k \end{align*}[/math]
yet? Here [math]\displaystyle f(x, y) = x^2y[/math] and [math]\displaystyle g(x, y) = x^2 + 2y^2 = 6[/math].
GWR309 said:f(x,y)=x^2y with the constraint of x^2+2y^2=6
Use lagrange multipliers to find the extrema.
Thanks!
GWR309 said:Yeah I tried. I ended up with 2y^2+sqrt(2)y-6 which doesn't seem right and if it is right, I don't know how to solve it
MarkFL said:The way I learned to use Lagrange multipliers, while Prove It is being more rigorous, is to write:
The objective function is:
$$f(x,y)=x^2y$$
subject to the constraint:
$$g(x,y)=x^2+2y^2-6=0$$
Now, first find the implications of the system:
$$f_x(x,y)=\lambda g_x(x,y)$$
$$f_y(x,y)=\lambda g_y(x,y)$$
Then use the implications in the constraint to find the critical points. Can you write down the system from which to take the implications?