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Review

# Review - Sections 4.1 4.2 4.3 and 4.4 Review Theory...

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Sections 4.1, 4.2, 4.3, and 4.4: Review Theory Instructor: Ms. Hoa Nguyen 4.1 Critical Numbers To ﬁnd critical numbers of a function f : - 1. Find the derivative f 0 ( x ). - 2. Find the critical numbers in the domain of f by considering 2 cases: f 0 ( x ) = 0 and f 0 ( x ) does not exist. The Closed Interval Method To ﬁnd the ABSOLUTE maximum and minimum values of a continuous function f on a closed interval [ a,b ], do the following steps: - 1. Find the critical numbers in ( ) and their f-values. - 2. Find the values of f at the endpoints of the interval. - 3. Compare the f-values: The largest value from steps 1 and 2 is the absolute maximum value. The smallest is the absolute minimum value. Local Maximum or Minimum Given a graph of a function f on its domain D , to know if f has a LOCAL max or min at x = c , ﬁrst we pick an open interval containing c and lying inside the domain D . - If we cannot pick such an interval, f does not have local max or min at x = c . This means that f NEVER has local max or min at the endpoints of the domain D .

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Review - Sections 4.1 4.2 4.3 and 4.4 Review Theory...

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