✔ 最佳答案
1. xlogx > x4/1000
log(xlogx) > log(x4) - log(1000)
(logx)(logx) > 4logx - 3
(logx)2 - 4logx + 3 > 0
(logx - 3)(logx - 1) > 0
logx > 3 或 logx < 1
x > 1000 或 x < 10
2. f(x)=2x2 - 4x + 6
f(x) = 2(x - 1)2 + 4
f(x) 最小值位於x=1, 其時f(x) = 4
(1)x屬於R
f(x) 最小值為4 => f(x) >= 4
(2)x>=2
f(2) = 6
f(x) >= 6
(3) -2 <= x <= 0
f(-2) = 22
f(0) = 6
4 <= f(x) <= 22
3. f(x) = |x2 - 4| - 3x
情況一: x2 - 4 > 0
x > 2 或 x < -2 (不切題)
f(x) = x2 - 3x - 4 = (x - 3/2)2 - 25/4
範圍不包括最小值的點
f(2) = -6
f(5) = 6
情況二: x2 - 4 <= 0
-2 <= x <= 2
f(x) = -x2 + 4 - 3x = -(x + 3/2)2 + 25/4
最大值位於 x = -3/2其值為25/4
f(-2) = 6
f(2) = - 6
f(x)在-2<=x<=5的最大值為25/4最小值為-6
4. f(x) = (2x2 - 2x + 3) / (x2 - x + 1)
f(x) = 2 + 1 / (x2 - x + 1)
= 2 + 1 / [(x - 1/2)2 + 3/4]
當x趨於+/-無限大時，f(x) = 2
當x = 1/2, f(x) = 2 + 4/3 = 10/3
f(x) 的最小值為2,最大值為10/3
2009-10-10 23:58:30 補充：
直接相除:
(2x^2 - 2x + 3) / (x^2 - x + 1)
= [2(x^2 - x + 1) +１] / (x^2 - x + 1)
= 2 + [ 1/ (x2 - x + 1)]
