一个关于导数的疑惑f(x)=(sinx-cosx)/x=√2sin(x-π/4)/x,导数f'(x)=(cos(x-π/4)x-sin(x-π/4))/x^2,x∈（π/4,3π/4）,此时cos(x-π/4),sin(x-π/4)都为正数,那么x=tan(x-π/4)不应该是f(x)的极小值吗.可为什么答案是极大

Question

一个关于导数的疑惑
f(x)=(sinx-cosx)/x=√2sin(x-π/4)/x,导数f'(x)=(cos(x-π/4)x-sin(x-π/4))/x^2,x∈（π/4,3π/4）,此时cos(x-π/4),sin(x-π/4)都为正数,那么x=tan(x-π/4)不应该是f(x)的极小值吗.可为什么答案是极大值呢?在线等,求解答!

Answer 1

纠正一下：f'(x)=√2(cos(x-π/4)x-sin(x-π/4))/x^2
其次,x>tan(x-π/4)时,f'(x)>0 而x∈（π/4,3π/4）时,x先>tan(x-π/4),后逐渐