推 nasmithed:清楚明瞭!!!謝謝!!!!!!!!!!!!! 115.43.46.168 07/05 22:33
※ 引述《nasmithed (飛機頭)》之銘言：
: x t^2-4
: y=∫ ----------- dt
: 0 1+(cost)^2
: 求x，讓y有最大值
: 我是先整個對x微分，令=0，求得x=2，-2
: 接下來套進去我就不會了....
: 化整後前面的 t^2 整個不會做呀.....
: --------
: (sint)^2
: 我記得要小角度上式才會等於1吧@@
: 請各位大大幫忙囉
: 感激不盡
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.
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◆ From: 114.34.122.244
※ 編輯: rygb 來自: 114.34.122.244 (07/05 10:22)