Re: [微積] 兩曲線公切線

看板Math作者mack (腦海裡依然記得妳)時間13年前 (2012/12/28 23:22)推噓2(2推 0噓 3→)

留言5則, 2人參與討論串2/3 (看更多)

※ 引述《stranger522 (香菇勇)》之銘言： : y=x^2 : y=-x^2+10x-17 : 求兩曲線的公切線 : 不知怎麼下手..有請各位高手~ y = x^2 y = -(x-5)^2+8 公切線:(y-4) = m(x-5/2) => y = mx - 5m/2 + 4 與 y = x^2 交於一點 => x^2 = mx - 5m/2 + 4 => x^2 - mx + (5m/2 - 4) = 0 唯一解 => D = (-m)^2 - 4 * 1 * (5m/2 - 4) = 0 => D = m^2 - 10m + 16 = (m - 2)(m - 8) = 0 => m = 2 or 8 => 公切線:y = 2x-1 or y = 8x-16 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 111.252.216.188

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stranger522

12/28 23:42, , 1^F

12/28 23:42, 1^F

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mack

12/28 23:44, , 2^F

12/28 23:44, 2^F

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stranger522

12/28 23:54, , 3^F

12/28 23:54, 3^F