# How do you find points of inflection and determine the intervals of concavity given #y=(3x+2)/(x-2)#?

##### 1 Answer

There are no points of inflection.

The interval of concavity is

#### Explanation:

Calculate the first derivative

This is a quotient

Here,

Therefore,

And the second derivative is

The points of inflection are when

Here, the second derivative is

So, there are no points of inflection

Build a sign chart for the concavity

The interval of concavity is

graph{(3x+2)/(x-2) [-41.1, 41.08, -20.56, 20.56]}