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Unformatted text preview: vu (tv2894) – Homework 13 (Section 4.1) – miner – (55096) 1 This print-out should have 6 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points If f is the function whose graph is given by 2 4 6 2 4 6 which of the following properties does f NOT have? 1. local minimum at x = 4 2. lim x → 4 f ( x ) = 4 3. f ′ ( x ) > 0 on (2 , 4) 4. local maximum at x = 2 correct 5. lim x → 2 + f ( x ) = lim x → 2- f ( x ) Explanation: The given graph has a removable disconti- nuity at x = 4. On the other hand, recall that f has a local maximum at a point c when f ( x ) ≤ f ( c ) for all x near c . Thus f could have a local maximum even if the graph of f has a removable discontinuity at c ; simi- larly, the definition of local minimum allows the graph of f to have a local minimum at a removable disconituity. So it makes sense to ask if f has a local extremum at x = 4. Inspection of the graph now shows that the only property f does not have is local maximum at x = 2 ....
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This note was uploaded on 11/07/2010 for the course M 408N taught by Professor Gualdini during the Fall '10 term at University of Texas.
- Fall '10