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.

Multivariable Calculus
Danielatia123 Danielatia123
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  • Mathe Mathe
    +1

    Is g continuous?

    • Danielatia123 Danielatia123
      0

      We don't know. Any way its not a given

    • Mathe Mathe
      0

      Got it! No assumption on g!

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Mathe Mathe
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  • Danielatia123 Danielatia123
    0

    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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