Question

若函数f(x)=x/(x^2+m)在x=1处取得极值,m的值为?

Answer 1

对f(x)求导,

f'(x)=[x*1/(x^2+m)]'=1/(x^2+m)-2x^2/(x^2+m)^2

因为在x=1处取得极值,即x=1时,f'(x)=0

所以,1/(m+1)-2(m+1)^2=0

解得：m=1