Question

求函数f(x)=2^x+log2x在区间[1.2]上的最大值和最小值

Answer 1

令g(x)=a^x,h(x)=loga^(x+1),则

容易判断,对于同一个a值,g(x)和h(x)的单调性是相同的.

g(x)和h(x)同时取最大值和最小值,且都是区间端点值.

则:

f(0)=g(0)+h(0)=1+loga^(0+1)=1;

f(1)=g(1)+h(1)=a+loga (1+1)=a+loga 2.

则:

1+(a+loga 2)=a;

loga 2=-1;

a=1/2