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函数f(x)=sinx-tanx,x属于[-π/4,π/4] 求值域
答案是[-根号2/2-1/2,根号2/2+1/2]
人气:474 ℃ 时间:2020-04-07 10:55:06
解答
答案写错了吧!
f(x) = sinx – tanx
求导:f ′(x) = cosx - 1/cos²x = (cos³x-1)/cos²≤0,定义域上单调减
在区间【-π/4,π/4】
最小值f(π/4) = sinπ/4 - tanπ/4 = √2/2 - 1
最大值f(-π/4) = sin(-π/4) - tan(-π/4) = -√2/2 + 1
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