x^2-2x-3<=0
(x-3)(x+1)<=0
得-1<=x<=3.
y=2^(x+2)-2*4^x=4*2^x-2*(2^x)^2
令t=2^x,-1<=x<=3,则有1/2<=t<=8.
故y=4t-2t^2=-2(t-1)^2+2
当t=1时即x=0时,有最大值=2,当t=8时即x=3时,有最小值=-96.