query 29

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course Mth 173

8/5/13 around 11 am

029. `query 29

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Question: `qQuery 3.10.23 (previously 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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Your solution:

the derivative of f(x) is <0. Therefore the function is decreasing on the interval. f(x) is greater than 0, then g(x)-h(x) is greater than 0 over that interval.

confidence rating #$&*:3

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Given Solution:

`aSince 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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Self-critique (if necessary):OK

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Question: `qQuery Add comments on any surprises or insights you experienced as a result of this assignment.

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Your solution:

I was surprised about the assignment length, but I think it was a good ending assignment

confidence rating #$&*:3

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Given Solution:

`aI 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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Self-critique (if necessary):OK

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&#Good responses. Let me know if you have questions. &#