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当0≤x≤π/2,f(x)=sinx-cosx的最大值、最小值
人气:223 ℃ 时间:2020-10-02 01:43:32
解答
f(x) = sinx - cosx
= √2 sin(x - π/4)
0 ≤ x ≤ π/2
-π/4 ≤ x - π/4 ≤ π/4
-1/√2 ≤ sin(x - π/4) ≤ 1/√2
-1 ≤ √2 sin(x - π/4) ≤ 1
-1 ≤ f(x) ≤ 1
最小值:-1
最大值:1
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