Critical points of a Hyperbolic function

[trojansc82]

Homework Statement

I am trying to find the critical points of the following hyperbolic function:

f(x) = a / (b + x)

Homework Equations

Critical points--> where f '(x) = 0

One of the points on the graph is a/2b

The Attempt at a Solution

I am not sure how to proceed with this question.

f '(x) = -a / (b + x)²

I attempted the quadratic formula with just the denominator, and the solution I came up with was x = -1.

 

[vela]

Did it occur to you the function may not have any critical points?