(1)
不妨取ωx₁+φ = -π/2,ωx₂+φ = π/2 (-π/2,π/2為相鄰對(duì)稱軸)
ωx₂+φ - (ωx₁+φ) = ω(x₂ - x₁) = ωπ/2 = π/2 - (-π/2) = π
ω = 2
最高點(diǎn)y = 4,A = 4
x = 5π/12,y取最大值,ω(5π/12) + φ = π/2,5π/6 + φ = π/2,φ = -π/3
f(x) = 4sin(2x - π/3)
f(x)周期為π
x = 5π/12 + nπ時(shí),y取最大值
x = -π/12 + nπ時(shí),y取最小值
x∈(-π/12 + nπ,5π/12 + nπ),單調(diào)增
x∈(5π/12 + nπ,11π/12 + nπ),單調(diào)減
(2)
5π/12在[π/4,π/2]內(nèi),函數(shù)f(x)的最大值=4
f(π/4) = 4sin(π/2 - π/3) = 4sin(π/6) = 2
f(π/2) = 4sin(π - π/3) = 2√3 > f(π/4)
最小值2