Question

已知函数f(x)=x2+kx+1 / x 2+1 若当x>0时,f(x)的最小值为-1,求实数k的值

Answer 1

f(x)=x2+kx+1 / x 2+1

=1+ kx / x 2+1

=1+ k/(x+1/x)

x>0

x+1/x>=2

则

1+k/2=-1

k=-4