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  • 求下列函數(shù)的最小正周期,遞增區(qū)間及最大值

    求下列函數(shù)的最小正周期,遞增區(qū)間及最大值
    (1)y=2sin2xcos2x
    (2)y=2cos的平方x/2+1
    (3)√3cos4x+sin4x
    數(shù)學(xué)人氣:278 ℃時(shí)間:2019-08-22 12:34:00
    優(yōu)質(zhì)解答
    y = 2 sin2x cos2x
    y = sin4x
    T = 2π/4 = π/2
    ymin = -1 at 4x = 2kπ - π/2
    ymax = 1 at 4x = 2kπ + π/2
    遞增區(qū)間[kπ/2 - π/8,kπ/2 + π/8],k∈Z
    ------------------------------------------------------------
    y = 2 cos²(x/2) + 1
    y = 1 + cosx + 1
    y = cosx + 2
    T = 2π
    ymin = 2 - 1 = 1 at x = 2kπ - π
    ymax = 2 + 1 = 3 at x = 2kπ
    遞增區(qū)間[2kπ - π,2kπ],k∈Z
    --------------------------------------------------------------------
    y = sin4x + √3 cos4x
    y = 2 sin(4x + π/3)
    T = 2π/4 = π/2
    ymin = -2 at 4x + π/3 = 2kπ - π/2,x = kπ/2 - 5π/24
    ymax = 2 at 4x + π/3 = 2kπ + π/2,x = kπ/2 + π/24
    遞增區(qū)間[kπ/2 - 5π/24,kπ/2 + π/24],k∈Z
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