Question

式子x乘以根号下(1-x^2)的最大值是---,此时x=--

Answer 1

先求x^2(1-x^2)的最大值

x^2(1-x^2)≤{[x^2+(1-x^2)]/2}^2=1/4

当且仅当x^2=1-x^2时成立

所以-1/2≤x√(1-x^2)≤1/2

所以x√(1-x^2)最大值=1/2

此时x^2=1-x^2且x>0

所以x=√2/2