Optimization, Step 3: Extreme Value Theorem

We can finally get to the point. The extreme value theorem is a fundamental theorem about continuous functions that most engineers don’t learn. Most engineering math courses use what’s valuable and hence skip out on a lot of details covered by other courses. That’s okay, because the situation is being rectified here. The extreme value theorem is rather simple. Bernard Bolzano and Karl Weierstrass made a much more complete version that we will be using in higher dimensions. We’re restricting ourselves to the one dimensional case still, and so we’ll just call it the extreme value theorem for now.
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