已知函数f(x)=2cos(π/2x+π/5),若实数x1,x2满足f(x1)-f(x2)=4,则(x1-x2)的绝对值的最小值是

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已知函数f(x)=2cos(π/2x+π/5),若实数x1,x2满足f(x1)-f(x2)=4,则(x1-x2)的绝对值的最小值是

已知函数f(x)=2cos(π/2x+π/5),若实数x1,x2满足f(x1)-f(x2)=4,则(x1-x2)的绝对值的最小值是
已知函数f(x)=2cos(π/2x+π/5),若实数x1,x2满足f(x1)-f(x2)=4,则(x1-x2)的绝对值的最小值是

已知函数f(x)=2cos(π/2x+π/5),若实数x1,x2满足f(x1)-f(x2)=4,则(x1-x2)的绝对值的最小值是
f(x)=2cos(π/2x+π/5)
f(x1)-f(x2)=2cos(π/2x1+π/5)-2cos(π/2x2+π/5)= 4
cos(π/2x1+π/5)-cos(π/2x2+π/5) = 2
∵-1 ≤ cos(π/2x1+π/5) ≤ 1,-1 ≤ cos(π/2x2+π/5) ≤ 1
∴ cos(π/2x1+π/5) = 1,cos(π/2x2+π/5) = - 1
π/2x1+π/5 = 2kπ,π/2x2+π/5=2kπ±π
x1+2/5 = 4k,x2+2/5=4k±2
x1 = 4k-2/5,x2=4k-2/5±2
|x1- x2| =|±2| = 2

由f(x)的式子可知它的周期是4,f(x1)-f(x2)=4可知x1,x2最小相差半个周期,所以答案应该是2、、、应该是这么做的,嘻嘻、、