Assn 29

course Mth173

Calculus I12-05-2007

Your work has been received. Please scroll through the document to see any inserted notes (inserted at the appropriate place in the document, in boldface) and a note at the end. The note at the end of the file will confirm that the file has been reviewed; be sure to read that note. If there is no note at the end, notify the instructor through the Submit Work form, and include the date of the posting to your access page.

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20:31:57

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20:44:39

Query 4.7.24 (was problem 7 p 290 ) prove if g' < h' on (a,b} and g(b) = h(b) then h < g on (a,b)--g,h both cont on [a,b] diff on (a,b)Explain why you expect, that for the given conditions, the function h will be strictly less than the function g on the interval.

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This looks like racetrack principal, so I will try and explain it like the book does. If g'

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20:45:12

Since f ' (x) < 0 on the interval the function is decreasing on the interval, hence since f(b) = 0 it follows that f(x) > 0 on the interval.

From this it follows that g(x) - h(x) > 0 on the interval and g(x) > h(x). **

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okay

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20:51:03

Query Add comments on any surprises or insights you experienced as a result of this assignment.

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I think I understand the principals described in the chapter and the racetrack principal.

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20:51:30

I was surprised (but not disappointed) that the query was only on one question. I did gain insight in that after I first typed in my original answer, I realized that it was wrong. I had proved (quite successfully, I thought) that the Racetrack principle was wrong! I'm hoping that my revised answer is more correct.

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okay

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This looks very good. Let me know if you have any questions. &#