(1) f(x)是y = √2sinx向左平移π,再向上平移√2/2得到的.
y = √2sinx在(π/2 +2kπ,3π/2 + 2kπ)内递减,f(x)在(π/2 - π/6 +2kπ,3π/2 - π/6 + 2kπ),即(π/3 +2kπ,4π/3 + 2kπ)内递减
(2)
x在[π/4,7π/6]
f(x)在[π/4,π/3)内递增,在 (π/3,7π/6)内递减
最大值:f(π/3)＝ √2sin(π/3 + π/6) + √2/2 = 3√2/2
x = π/4比x = 7π/6离对称轴x = π/3更近,最小值:f(7π/6) = √2sin(7π/6 + π/6) + √2/2 = (√2 - √6)/2