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Homework Statement
Find the absolute extrema of the function on the set D.
f(x,y)= x^2 + 4y^2 + 3x -1
D= {(x,y) l x^2 + y^2 ≤ 4}
Homework Equations
The Attempt at a Solution
The only thing I've done so far was find the critical point. I found f-sub x = 2x+3 and f-suby= 8y giving me a critical point of (-3/2,0), correct?
Using that critical point, I found f(-3/2,0) = -1
After that, I don't know how to proceed. I know -2 ≤ x ≤ 2 and -2 ≤ y ≤ 2 but how do I find the other critical numbers with that info? I'm unsure because the closed boundary graph is a circle and not a square, box, or triangular region.