MATH 1680 Lecture Notes - Lecture 1: Minimax
Math 1680-80 Lecture 14
Recall
Last week's lesson was on finding intervals where increases/decreases (sign of tells
this)
Today
Optimization
Finding max/min of ( will be the key)
Terminology:
Note: if is continuous then all max and min happen at critical numbers.
Continuity on closed
are also possible
– critical numbers
absolute min
relative min
absolute maximum
Document Summary
Last week"s lesson was on finding intervals where (cid:4666)(cid:4667) increases/decreases (sign of (cid:4666)(cid:4667) tells. Finding max/min of (cid:4666)(cid:4667) ( (cid:4666)(cid:4667)=(cid:882) will be the key) Optimization absolute maximum relative min absolute min (cid:1853) (cid:1854) Note: if (cid:4666)(cid:4667) is continuous then all max and min happen at critical numbers. Continuity on closed [(cid:1853),(cid:1854)] (cid:4666)(cid:1854)(cid:4667) (cid:1854) (cid:1853) (cid:4666)(cid:1853)(cid:4667),(cid:4666)(cid:1854)(cid:4667) are also possible. (cid:4666)(cid:1855)(cid:4667) does not exist are also candidates for critical numbers: example: find max on [ 1,3] the critical numbers: (cid:4666)(cid:4667)=(cid:2870) Conclusion: abs min at =(cid:882) and is = 0, abs ma at =(cid:885) and is = 9. Side note: if the intervals open, ex: ( 8, 3), then the max/min is + and . there is no actual (cid:4666)(cid:4667)=(cid:2870)(cid:2871) Conclusion: absolute max at =(cid:890) and it is 4. Abs min at =(cid:882) and it is 0: example; a piece of wire is length 12 units. You need to bond the wire to a rectangular shape.
