Question

函数y=2sin(兀x/6-兀/3)(0<=x<=9)的最大值与最小值之和为

Answer 1

y=2sin(πx/6
-π/3)周期T=2π/(π/6)=12
令2kπ-π/2
≤πx/6
-π/3≤2kπ+π/2
解
12k-1≤x≤12k+5k整数
y[05]增函数[5,9]减函数
所
x=5y值2
x=0y值-√3
值值2-√3.
或者:1≤x≤9
所
π/6-π/3
≤πx/6
-π/3≤9π/6-π/3
即
-π/6
≤πx/6
-π/3≤7π/6
πx/6
-π/3=π/2y值2
πx/6
-π/3=-π/6y值--√3
值值2-√3.