第十二题求解谢啦要详细过程
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(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
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
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