作者GBRS ()
看板trans_math
标题Re: [微分] 94政大风管
时间Wed Jan 16 12:17:33 2008
※ 引述《bitchdog (超人会隐形)》之铭言：
: Use any method you like to find the local minimum and
: local maximum of the following functin :
: f(t)= sint
: ------ , t<2π
: 2+cost
用半角代换做吧!
令u=tan(t/2),t=2arctanu,-π <= t <= π
则sint=2u/(1+u^2),cost=(1-u^2)/(1+u^2)
所以f(u)=[2u/(1+u^2)]/{2+[(1-u^2)/(1+u^2)]}
=2u/(3+u^2)
=>f'(u)=2(3-u^2)/(3+u^2)^2=0
解得u=sqrt3 or -sqrt3
刚好可配一个local max.与另一个local min.
--
※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 211.76.57.219
1F：推 david7834:这种解法也很好^^ 61.225.194.65 01/16 12:27