Question

函数f(x)=x+1/x在区间（0,1]上是单调减函数,在区间[1,+无穷大）上是单调增函数

Answer 1

f(x)=x+1/x,f'(x)=1-1/x^2,当x∈（0,1]时,f'(x)＜0,当x[1,+无穷大）时,f'(x)≥0,命题得证