求解sqrt(x^4-15x^2-8x+80)-sqrt(x^4-3x^2+4)的最大值?
回答 (2)
2019-03-14 8:35 pm
✔ 最佳答案
"(P1) 求解sqrt(x^4-15x^2-8x+80)-sqrt(x^4-3x^2+4)的最大值 和(P2) 求解{ (x^4-15x^2-8x+80)-(x^4-3x^2+4)} 的最大值" 是等同 equivalent的，這麼說是因為成就(P1) 的x=x*也是成就(P2) 的x=x*，且反之亦然。於是先解(P2)求得x=-1/3;再代入原問題(P1)即可。
2020-02-25 8:56 pm
Let f=x^4-15x^2-8x+80, g=x^4-3x^2+4, find Max h(x) = f^0.5 - g^0.5
Set h'(x) = f/2f^0.5 - g/2g^0.5 = 0 to find max
given f^0.5 / g^0.5 = f / g = k
=> f^0.5 = k*f, g^0.5 = k*g
=> Max h(x) = Max k*(f - g) = Max -4(3x^2 + 2x - 19)
=> at xc = (58^0.5 - 1)/3 having max
=> Max h(xc) = ........
Set h'(x) = f/2f^0.5 - g/2g^0.5 = 0 to find max
given f^0.5 / g^0.5 = f / g = k
=> f^0.5 = k*f, g^0.5 = k*g
=> Max h(x) = Max k*(f - g) = Max -4(3x^2 + 2x - 19)
=> at xc = (58^0.5 - 1)/3 having max
=> Max h(xc) = ........
收錄日期: 2021-04-30 20:00:35
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20190313132443AAERNEx