- #1
Mathoholic!
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Homework Statement
f(x,y)=2x3-2y3-3x2
K={(x,y)[itex]\in[/itex]ℝ2:x2+y2≤5,y≤0}
Find the maximum and minum of f(x,y) within K.
Homework Equations
∇f(x,y)=(6x2-6x,-6y)
Hess(f)=diag(12x-6,-6) (relevant?)
The Attempt at a Solution
What I've done so far was calculate the pair(s) (x,y) that make ∇f(x,y)=(0,0).
It gave me: (0,0) and (1,0).
Now, both these points belong to K (a semicircle), thus, I would assume them to be good candidates but they're not.
The solution to the problem is: (√5,0) and (-√5,0).
Am I doing something wrong? How do I proceed about when presented with maxima and minima confined to a limited region of space?