IND ENG 160 Lecture Notes - Lecture 3: Stationary Point, Saddle Point, Univariate
14 Dec 2017
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Document Summary
The goal is to min / max f (x) such that x satis es some arbitrary number of constraints, where f (x) is the objective function: constrained. A stationary point is a point that is locally at. This is equivalent to saying that the rst derivative is 0 at that point. Finding local minima and maxima is important for optimization. The univariate case is considered here, but the insights can be generalized to the multivariate case. We need to classify the di erent stationary points by their second derivative if the rst derivative is 0, and it is not an endpoint. This is because just knowing that the rst derivative is 0 does not tell us which way the function is curved at that point. Given that we know that f (x) = 0. f f f (x) > 0 local min (x) < 0 local max (x) = 0 need to check the third derivative.
