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review3 - MAT125 Fall 2007 Review for Final Examination The...

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MAT125 Fall 2007 Review for Final Examination The Final Exam is cumulative, so the review sheets for Midterm 1 and for Midterm 2 should be used along with the following. 4.1 Work through Examples 1, 2, 3, 4, 5 understanding how they reflect the “Strategy” explained on p.265. Exercises 4, 9, 18 and as many others as you can fit in. 4.2 Understand the definitions (Box 1, p.269) of “ f has an absolute maximum at c ” and “ f ( c ) is the maximum value of f ” (and for “minimum” also). Understand the definition (Box 2, p270) of “ f has a local maximum at c ,” etc. and study Example 4 carefully. Understand what Fermat’s Theorem says (Box 4, p.272) and the situations of Figure 9 (you can have f 0 ( c ) = 0 without c being a local max or min) and Figure 10 ( f might not have a derivative at the point c where f ( c ) is minimum or maximum) . Be able to implement the “Closed Interval Method” (Box, p.273): Example 7, Exercises 5, 19, 25, 39. 4.3 Understand that if f 0 ( x ) > 0 on an interval, then f is “sloping up” and

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