#$&*
course MTH 173
6/12/2013
029. `query 29
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Question: `qQuery 3.10.23 (previously 4.7.24) (was problem 7 p 290 ) prove if g' < h' on (a,b} and g(b) = h(b) then h < g on (a,b)--g,h both cont on [a,b] diff on (a,b)Explain why you expect, that for the given conditions, the function h will be strictly less than the function g on the interval.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
f ' (x) < 0 on the interval the function is decreasing on the interval
f(b) = 0 it follows that f(x) > 0 on the interval.
It follows that g(x) - h(x) > 0 on the interval and g(x) > h(x).
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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). **
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
Self-critique (if necessary):
OK
------------------------------------------------
Self-critique Rating:
#$&*
course MTH 173
6/12/2013
029. `query 29
*********************************************
Question: `qQuery 3.10.23 (previously 4.7.24) (was problem 7 p 290 ) prove if g' < h' on (a,b} and g(b) = h(b) then h < g on (a,b)--g,h both cont on [a,b] diff on (a,b)Explain why you expect, that for the given conditions, the function h will be strictly less than the function g on the interval.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
f ' (x) < 0 on the interval the function is decreasing on the interval
f(b) = 0 it follows that f(x) > 0 on the interval.
It follows that g(x) - h(x) > 0 on the interval and g(x) > h(x).
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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:
#*&!
&#Good work. Let me know if you have questions. &#