# How do you sketch the curve #y=x+1/x# by finding local maximum, minimum, inflection points, asymptotes, and intercepts?

##### 1 Answer

Please see the explanation.

#### Explanation:

Here is a graph of the curves:

graph{x+1/x}

The first derivative is:

To obtain the x coordinates of local extrema, set that equal to zero:

Perform the second derivative test:

It is positive for

This makes the point

Outside of that domain, the curve resembles the line