已知函数f(x)=Asin(wx+b)+k,x∈R(其中A>0,W>0,0

1个回答

  • (Ⅰ)由最低点为M(2π/3,-2)得A=2由T=π

    得ω=2π/T=2π/π=2

    由点M(2π/3,-2)在图象上得

    2sin(4π/3+φ)=-2即sin(4π/3+φ)=-1

    所以4π/3+φ=2kπ-π/2

    故φ=2kπ-11π/6 (k∈Z)

    又φ∈(0,π/2),所以φ=π/6

    所以f(x)=2sin(2x+π/6)

    (Ⅱ)因为x∈[0,π/12],可得2x+π/6∈[π/6,π/3]

    所以当2x+π/6=π/6时,即x=0时,f(x)取得最小值1;

    当2x+π/6=π/3,即x=π/12时,f(x)取得最大值√3 .