孤立点的定义:y=-acos2x-√3asin2x+2a+b,a>0,x∈[0,π]

来源:百度文库 编辑:杭州交通信息网 时间:2024/04/28 16:12:48
-5≤y≤1,t∈[-1,0],g(t)=at^+bt-3的最小值

y=-acos2x-√3asin2x+2a+b
=-2a*(1/2*cos2x+√3/2*sinx)+2a+b
=-2a*(sinπ/6*cos2x+cosπ/6*sinx)+2a+b
=-2a*sin(2x+π/6)+2a+b

-1<=sin(2x+π/6)<=1
所以:-2a+2a+b<=y<=2a+2a+b
b<=y<=4a+b,
因为-5≤y≤1,
所以 :b=-5,4a+b=1.
a=3/2,b=-5.

g(t)=3/2*t^2-5t-3,t∈[-1,0],
g(t)=3/2(t-5/3)^2-43/6, t∈[-1,0]

当t=0时,g(t)有最小值g(0)=-3.