Question

若指数函数x^2-2x-3小于等于0,求函数y=2^(x+2)-2^(2x+1)的最值

Answer 1

x^2-2x-3≤0

(x+1)(x-3)≤0

-1≤x≤3

y=2^(x+2)-2^(2x+1)

=4*2^x-4*2^2x

设2^x=t∈[1/2,8]

y=-4t^2+4t

=-4(t-1/2)^2+1

当t=1/2时,最小值：1