作者beatitude (何时能入物理系?)
看板trans_math
标题Re: [微分]请教一题微分
时间Sun Jul 17 14:56:18 2005
※ 引述《nomindman ()》之铭言：
: Let g(x) = f(x*2) , where f is twice differentiable for all x ,
: f'(x) > 0 for all x ≠ 0 , and f is concave downward on
: (－∞ , 0 ) and concave upward on ( 0 , ∞ ) .
: (1) At what numbers does g have an extreme value ?
: (2) Discuss the concavity of g .
: 因为没有解答...请高手们帮我看看thx
f is concave downward on (－∞ , 0 ) and concave upward on ( 0 , ∞ )
-> f'' < 0 on (－∞ , 0 ) and f'' > 0 on ( 0 , ∞ )
g'(x) = 2xf'(x^2) 只有x=0 才有极值
g''(x) = (4x^2)f''(x^2) + 2f'(x^2)
﹏﹏﹏﹏﹏﹏﹏ ﹏﹏﹏﹏
>0 >0
so g is concave upward on R
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※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 218.168.242.213
1F：推 hotdave:我想问"只有X=0才有极值这"个理论是从哪来的 61.64.109.220 07/17
2F：推 beatitude:g'(x)=0 只有一解 x=0218.168.242.213 07/17
3F：推 hotdave:嗯，多谢!!! 61.64.109.220 07/17