作者Eliphalet (搞边样衰边样)
站内trans_math
标题Re: [考古] 95成大
时间Thu Jul 3 03:47:05 2008
※ 引述《linda1218 (linda)》之铭言：
: let f be a real valued function defined on R with f''>0 for all x
: show that f(x)>= f(0)+f'(0)x
由 Taylor Theorem , 当 x≠0 , 存在 ζ 介於 0 跟 x 之间
使得
f'(0) f"(ζ)
f(x) = f(0) + ------- * (x-0) + --------- * (x-0)^2
1! 2!
> f(0) + f'(0) * x
当 x = 0 , f(0) = f(0) + f'(0) * 0
所以
f(x) ≧ f(0) + f'(0) * x
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