query29

#$&*

course Mth 173

029. `query 29

*********************************************

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.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

f'(x)<0 when the function is decreasing because f(b)=0 meaning f(x)>0

So g(x)-h(x)>0 therefore g(x)>h(x)

confidence rating #$&*:3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

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). **

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):ok

------------------------------------------------

Self-critique Rating:ok

*********************************************

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

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

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.

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

------------------------------------------------

Self-critique Rating:

"

Self-critique (if necessary):

------------------------------------------------

Self-critique rating:

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