Question

f(x)=(x^2+2)/(根号下x^2+1)的最小值和此时的x值

Answer 1

f(x)=(x^2+1+1)/√(x^2+1)

=√(x^2+1)+1/√(x^2+1)

x^2+1>=1,所以√(x^2+1)>=1

f(x)=√(x^2+1)+1/√(x^2+1)>=2√[√(x^2+1)*1/√(x^2+1)]=2

当√(x^2+1)=1/√(x^2+1)时取等号

则x^2+1=1

x=0

所以x=0,f(x)最小=2