# What are the maximum and minimum values that the function #f(x)=x/(1 + x^2)#?

##### 1 Answer

Jun 21, 2015

Maximum:

Minimum:

#### Explanation:

An alternative approach is to rearrange the function into a quadratic equation. Like this:

Let

Recall that for all real roots of this equation the **discriminant is positive or zero**

So we have,

It is easy to recognise that

Hence,

This shows that the maximum is