Re: [微分]請教一題微分

看板trans_math作者beatitude (何時能入物理系?)時間20年前 (2005/07/17 14:48)推噓3(3推 0噓 0→)

留言3則, 2人參與討論串2/2 (看更多)

※ 引述《nomindman ()》之銘言： : 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 . : 因為沒有解答...請高手們幫我看看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 才有極值 g''(x) = (4x^2)f''(x^2) + 2f'(x^2) ﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏ >0 >0 so g is concave upward on R -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 218.168.242.213

推

hotdave

61.64.109.220 07/17, , 1^F

61.64.109.220 07/17, 1^F

推

beatitude

218.168.242.213 07/17, , 2^F

218.168.242.213 07/17, 2^F

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hotdave

61.64.109.220 07/17, , 3^F

61.64.109.220 07/17, 3^F