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## Main Question or Discussion Point

Hello, I'm trying to construct a function f from R^2 -> R where f is everywhere differentiable, doesn't have a local min at 0 but if I restrict the domain of f to any line through the origin, 0 will be a (strict) min at that point..

I've been fooling around with this, but I don't really have any good strategies for figuring out how to make this function. Any tips? thank you

I've been fooling around with this, but I don't really have any good strategies for figuring out how to make this function. Any tips? thank you