(1)由图像上一个最低点为M(2π/3,-2)可得A=2,
T=2π/ω=π,ω=2,
f(2π/3)=2sin(2x+φ)=-2,
2*2π/3+φ=3π/2,φ=π/6,
f(x)=2sin(2x+π/6).
(2)、x∈[0,π/12],函数单调递增,
最小值是f(0)=2sin(π/6)=1.
最大值=f(π/12)=2sin(π/3)=√3.
(3).对于f(x)=sinx单调递增区间,2kπ-π/2≤x≤2kπ+π/2,
2kπ-π/2≤2x+π/6≤2kπ+π/2,
kπ-π/3≤x≤kπ+π/6,
单调递减区间,2kπ+π/2≤x≤2kπ+3π/2,
2kπ+π/2≤2x+π/6≤2kπ+3π/2,
kπ+π/6≤x≤kπ+2π/3. (1)由图像上一个最低点为M(2π/3,-2)可得A=2,
T=2π/ω=π,ω=2,
f(2π/3)=2sin(2x+φ)=-2,
2*2π/3+φ=3π/2,φ=π/6,
f(x)=2sin(2x+π/6).
(2)、x∈[0,π/12],函数单调递增,
最小值是f(0)=2sin(π/6)=1.
最大值=f(π/12)=2sin(π/3)=√3.
(3).对于f(x)=sinx单调递增区间,2kπ-π/2≤x≤2kπ+π/2,
2kπ-π/2≤2x+π/6≤2kπ+π/2,
kπ-π/3≤x≤kπ+π/6,
单调递减区间,2kπ+π/2≤x≤2kπ+3π/2,
2kπ+π/2≤2x+π/6≤2kπ+3π/2,
kπ+π/6≤x≤kπ+2π/3.