已知函数f(x)=Asin(wx+φ)+A在x属于0,7π内取得一个最大值和最小值,且当x=π,y最大3,x=6π,y最小为-3

（1）A(>0)=3,周期2π/w=2(6π-π),w=1/5,当x=π时,取wx+φ=π/5+φ=π/2,得φ=3π/10,
此函数解析式为f(x)=3sin(x/5+3π/10)
（2）问题即是否存在实数m,满足不等式：sin{√[-(m-1)^2+4]/5+3π/10}＞sin[√(-m^2+4)/5+3π/10].
首先,-(m-1)^2+4>=0,-m^2+4>=0
即|m|<=2.|m-1|=2则-1=当-1=-m^2>-(m-1)^2>=-4,
-3π<3π/10=<√[-(m-1)^2+4]/5+3π/10<√(-m^2+4)/5+3π/10<=4/5+3π/10<2π,
f(x)在[-3π,2π]上递增,sin{√[-(m-1)^2+4]/5+3π/10}当1/22π>4/5+3π/10=>√[-(m-1)^2+4]/5+3π/10>√(-m^2+4)/5+3π/10>=3π/10>-3π,
f(x)在[-3π,2π]上递增,sin{√[-(m-1)^2+4]/5+3π/10}>sin[√(-m^2+4)/5+3π/10]
所以,存在实数m,满足不等式：sin{√[-(m-1)^2+4]/5+3π/10}>sin[√(-m^2+4)/5+3π/10],
m的取值范围为(1/2,2].