# Let #f(x) = x / (x^2+1)#, how do you use the first derivative test to determine which critical numbers, if any give relative extrema?

##### 1 Answer

The critical numbers are when

there is a minimum at

and a maximum at

#### Explanation:

The derivative of a quotient is

so

The denominator is always

so

Let's do a sign chart

so, there is a minimum at

Also, the limit of

limit

limit

Also,

graph{x/(x^2+1) [-2.222, 2.222, -1.111, 1.11]}