求求这个解题过程 在线等 急急急
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2022-01-26
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12. f(x) = (√3/2)cos2x + √3/2 +(1/2)sin2x - √3/2 = sin(2x+π/3)
单调增加区间 2kπ-π/2 ≤ 2x+π/3 ≤ 2kπ+π/2,
2kπ-5π/6 ≤ 2x ≤ 2kπ+π/6, kπ-5π/12 ≤ x ≤ kπ+π/12. k 为整数。
x ∈ [0, π/4] 时, f(0) = sin(π/3) = √3/2, f(π/4) = sin(5π/6) = 1/2,
最大值 f(π/12) = sin(π/2) = 1, 则 f(x) ∈ [1/2, 1] .
单调增加区间 2kπ-π/2 ≤ 2x+π/3 ≤ 2kπ+π/2,
2kπ-5π/6 ≤ 2x ≤ 2kπ+π/6, kπ-5π/12 ≤ x ≤ kπ+π/12. k 为整数。
x ∈ [0, π/4] 时, f(0) = sin(π/3) = √3/2, f(π/4) = sin(5π/6) = 1/2,
最大值 f(π/12) = sin(π/2) = 1, 则 f(x) ∈ [1/2, 1] .
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