Suppose that I need to find the global maximum of $f(x)$ but $f'(x)=0$ and $f''(x)=0$ can only be solved numerically. How do I am 100% sure that I have found the correct optimums. My doubt is because the algorithms do not find the roots with probability one.
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1Do you have some specific function in mind? – M. Winter Mar 20 '18 at 15:58
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Yes, this one. https://mathoverflow.net/questions/294712/unique-root-by-numerical-solution and that root is a maximum. – Quema Mar 20 '18 at 17:52