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Apr 10, 2020 at 12:59 comment added Roman You can never know if NMaximize gets stuck in a local extremum or finds the global one. Some of the options, like Method, can help greatly; also, doing a ContourPlot3D can give you an idea if there are any regions of higher values. For a rigorous answer you need to go to the math stackexchange.
Apr 10, 2020 at 10:54 comment added Natalia C. Thank you for your answer. Just wondering, how do you know the maximizer that NMaximize finds is a global maximizer? and how to rigorously show that the exact value must be Sin[π/8]? Thanks a lot.
Apr 10, 2020 at 10:46 history answered Roman CC BY-SA 4.0