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函数y=x² -2ax+1的定义域为(0,2),求值域
人气:120 ℃ 时间:2019-10-19 16:55:52
解答
y = x^2-2ax +1
y' = 2x-2a =0
x= a
y'' = 2 >0 (min)
case 1: a ≤ 0
y > y(0) = 1
y < y(2) = 5-4a
值域 ( 1,5-4a)
case 2: 0min y = y(a)
=a^2-2a^2+1
= -a^2+1
y(0) = 1
y(2) = 5-4a(max)
值域 (-a^2+1, 5-4a)
case 3: a≥2
yy> y(2)=5-4a
值域 ( 5-4a, 1)
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