作者rygb (再生)
看板trans_math
标题Re: [考古] 师大99
时间Tue Jul 5 10:21:09 2011
※ 引述《nasmithed (飞机头)》之铭言：
: x t^2-4
: y=∫ ----------- dt
: 0 1+(cost)^2
: 求x，让y有最大值
: 我是先整个对x微分，令=0，求得x=2，-2
: 接下来套进去我就不会了....
: 化整後前面的 t^2 整个不会做呀.....
: --------
: (sint)^2
: 我记得要小角度上式才会等於1吧@@
: 请各位大大帮忙罗
: 感激不尽
2
x - 4
y' = ------------ (by Leibniz Rule)
2
1 + cos x
and we find critical point ..
f'(x)= 0.
2
we know that cos x +1 > 0 (
always.)
so x = ±2 are critical point..
check the right side and left side of the critical point
2
x - 4 = 0 --- > (x + 2) (x - 2) = 0
x-intercept. x=2,-2
in the interval (2 ,∞) , (-∞, -2) is positive.
and interval (-2, 2) is negative.
for y'(x)
left right
postive -> negative , Maximum
negative -> postive , Minimum
so x =-2 is where y occur Maximum.
x = 2 is where y occur Minimum.
--
※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 114.34.122.244
※ 编辑: rygb 来自: 114.34.122.244 (07/05 10:22)
1F：推 nasmithed:清楚明了!!!谢谢!!!!!!!!!!!!! 115.43.46.168 07/05 22:33