Find the extreme values of f on the region described by the inequality. f(x,y) = 2x^2 + 3y^2 - 4x -9, x^2 + y^2 ≤ 16
I am very confused with the steps of how to approach these types of problems. I found..
-partial deriv of x: 4x-4
-partial deriv of y: 6y
Then, I followed an example in my book and found the critical point by setting those equations above to 0, getting x=1, y=0; so the point would be (1,0)
Then, use Lagrange multipliers like this
Here's where I get a little lost because I'm not really sure what to solve for (x,y, or λ?) and where/what I plug that into when I find it... I tried solving 6y=λ2y, getting λ = 3, then plugging it into x=4/4-2λ, but I don't think that's right.
Thank you so much for your help!