Question

求函数y=(log0.25^x)^2-log0.25^x+5,x为【2,4】的最小值和最大值.

Answer 1

函数y=(log0.25^x)^2-log0.25^x+5,x为【2,4】,

令,log0.25(x)=t,

当X=2时,log0.25(2)=t1,t1=-1/2,

当X=4时,log0.25(4)=t2,t2=-1.

∴t的取值范围是[-1,-1/2].

而,Y=t^2-t+5=(t-1/2)+19/4.此抛物线是开口向上,对称轴为t=1/2.

所以,Y的最大值是当t=-1时,Y最大是7,Y的最小值是当t=-1/2时,Y最小是23/4.