推 ccz0123 : 謝謝Z大的即時幫忙！小弟已經懂了！ 07/17 23:03
※ 引述《ccz0123 (ccz)》之銘言：
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: 大一微積分
: 求解 37、38
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: 小弟經濟狀況清寒
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<Rolle's Theorem>
If f is continous on [a,b] and differentiable on (a,b)
and f(a)=f(b)=0
Then there exists c€(a,b) such that f'(c) = 0
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[37]
Let f(t) = g(t)-h(t) the same as in the hint
Then g(0)=h(0) (start at the same time)
g(T)=h(T) (finish in a tie 平手=同時間抵達)
hence f(0)=f(T)=0, then by Rolle's thm we know f'(c) = 0
which implies g'(c)=h'(c)
Note: derivative of position function is speed
[38]
Assume there exist a,b two distinct points such that f(a)=a, f(b)=b
Let g(x)=f(x)-x, then g(a)=g(b)=0.
Hence by Rolle's thm we know g'(c)=f'(c)-1=0 => f'(c)=1, contradictory
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※ 編輯: znmkhxrw (111.255.19.59), 07/17/2017 22:34:39