Question

What are the absolute extrema of `f(x)=1/(1+x^2) in[oo,oo]`?

Answer 1

`x=0` is the maximum of the function.

Explanation:

`f(x)=1/(1+x²)`
Let's search `f'(x)=0`
`f'(x)=-2x/((1+x²)²)`
So we can see that there's an
unique solution, `f'(0)=0`
And also that this solution is a maximum of the function, because `lim_(x to ±oo) f(x)=0`, and `f(0)=1`
\0/ here's our answer!