Question

函数f（x）=a的x次方+log以a为底（x+1）在【0,1】上的最大值和最小值德赫为a,则a的值为?

Answer 1

当a＞1时,f(x)在[0,1]上单调递增

f(x)max=f(1)=a+log(a)2

f(x)min=f(0)=1

a+log(a)2+1=a

解得：a=1/2＜1,舍去

当0＜a＜1时,f(x)在[0,1]上单调递减

f(x)min=f(1)=a+log(a)2

f(x)max=f(0)=1

a+log(a)2+1=a

解得：a=1/2