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I wanted to know if the endpoints of an nth dimension linear equation will be guaranteed to contain a min and max over that interval.

For 1D ( like a line), if I find f(x) over an interval [x_{0}, x_{n}], I'm guaranteed that the two end points will be either an max or min.

So I was wondering if this applies to any nth dimension linear equation?

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# The extremes of an nth dimension linear equation

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