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

May 11, 2018

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

#### Explanation:

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