f(x)=2sin(π/4x+π/4)+2sin(π/4x+3π/4)在[-6,-2/3]上的最大值和最小值以及相应的x的值

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f(x)=2sin(π/4x+π/4)+2sin(π/4x+3π/4)在[-6,-2/3]上的最大值和最小值以及相应的x的值f(x)=2sin(π/4x+π/4)+2sin(π/4x+3π/4)在[-

f(x)=2sin(π/4x+π/4)+2sin(π/4x+3π/4)在[-6,-2/3]上的最大值和最小值以及相应的x的值
f(x)=2sin(π/4x+π/4)+2sin(π/4x+3π/4)在[-6,-2/3]上的最大值和最小值以及相应的x的值

f(x)=2sin(π/4x+π/4)+2sin(π/4x+3π/4)在[-6,-2/3]上的最大值和最小值以及相应的x的值
f(x)=2sin(π/4x+π/4)+2sin(π/4x+3π/4)
=2sin(π/4x+π/4)+2cos(-π/2+π/4x+3π/4)
=2sin(π/4x+π/4)+2cos(π/4x+π/4)
=2倍根号2*sin(π/4x+π/4+π/4)
=2倍根号2*sin(π/4x+π/2)
=2倍根号2*cos(π/4x)
∵x∈[-6,-2/3]
∴π/4x∈[-3π/2,-π/6]
∴cos(π/4x)∈[-1,根号3/2]
∴f(x)∈[-2倍根号2,根号6]
∴x=-4时,f(x)min=-2倍根号2
x=-2/3时,f(x)max=根号6

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