Yahoo Answers: Answers and Comments for 兩題 M.V.T. 證明題 [數學]
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From haha
enUS
Thu, 10 Dec 2009 23:05:12 +0000
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Yahoo Answers: Answers and Comments for 兩題 M.V.T. 證明題 [數學]
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https://answers.yahoo.com/question/index?qid=20091210000015KK08866
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From 六呎將軍: (1) f(4) = 1, f(1) = 1/4
f'(x) = 2/(x  ...
https://answers.yahoo.com/question/index?qid=20091210000015KK08866
https://answers.yahoo.com/question/index?qid=20091210000015KK08866
Fri, 11 Dec 2009 15:42:43 +0000
(1) f(4) = 1, f(1) = 1/4
f'(x) = 2/(x  3)3
Hence we have:
6/(c  3)3 = 1/4  1
6/(c  3)3 = 3/4
(c  3)3 = 8
c  3 = 2
c = 5 which is beyond 1 < x < 4
It does not contradict to the Mean Value Thm since f(x) is NOT differentiable at x = 3.
(2) f(3) = 3 and f(0) = 1
When x < 1/2, f(x) = 1 + 2x, f'(x) = 2
When x >= 1/2, f(x) = 3  2x, f'(x) = 2
So we have:
f(3)  f(0) = 4 which is not equal to 2 nor 2
It does not contradict to the Mean Value Thm since f(x) is NOT differentiable at x = 1/2