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

There are no points of inflection.

The interval of concavity is

Determine the initial derivative.

Here,

Consequently,

Furthermore, the second derivative is

Thus, there aren't any turning points.

Create a concavity sign chart.

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

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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