How do you sketch the curve #y=x+1/x# by finding local maximum, minimum, inflection points, asymptotes, and intercepts?
Please see the explanation.
Here is a graph of the curves:
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