Question

求f(x)=-4^x+3*2^x+1在【1,2】上值域

Answer 1

f(x)=-4^x+3*2^x+1

=-2^2x+3*2^x+1

=-(2^x-3/2)^2+13/4

∵1≤x≤2

∴2≤2^x≤4

∴函数在[1,2]上是减函数.

则当2^x=2时函数有最大值3.

当2^x=4时函数有最小值-3/4