Existence of golobal minimum point for continuous functions on $\mathbb{R}^2$
Let
1. $g:[0,\infty)\rightarrow \mathbb{R}$ such that $\lim_{t\rightarrow \infty}g(t)=\infty$
2. $f: \mathbb{R}^2\rightarrow \mathbb{R}$ continues such that for all (x,y): f(x,y) $\geq$ g($\sqrt{x^2+y^2} $ ).
Prove that f has a global minimum point.
1. $g:[0,\infty)\rightarrow \mathbb{R}$ such that $\lim_{t\rightarrow \infty}g(t)=\infty$
2. $f: \mathbb{R}^2\rightarrow \mathbb{R}$ continues such that for all (x,y): f(x,y) $\geq$ g($\sqrt{x^2+y^2} $ ).
Prove that f has a global minimum point.
Answer
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Mathe
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In line 7 I'm not sure how f(x min,y min) can be little/equal to c if for all (x,y) f(x,y)>=g((x^2+y^2)^0.5) and g>c?
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Nevermind. I got it
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The answer is accepted.
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Is g continuous?
We don't know. Any way its not a given
Got it! No assumption on g!