Q: upgrade to El Capitan and wanted to use AHT

Depending on the age of your Mac, it may not exist as a partition on your disk. In that case it would be on your OEM install DVD.

Using Apple Hardware Test - Apple Support

Apple Hardware Test

Apple Hardware Test – Invoke and Interpret

Apple Hardware test – How to run and interpret (2)

Apple Hardware Test - Using

Apple Diagnostics – Computers introduced after June 2013

Apple Diagnostics: Reference codes

You'll need the install DVDs, if you no longer have them call Apple and give them your serial number and they will ship them to you for a nominal fee.

Using Apple Hardware Test on computers with OS X v10.7 and earlier

AHT is located on the Applications Install Disc 2 and should be included with your computer or the MacBook Air Software Reinstall Drive on a MacBook Air (Late 2010). To start AHT on these computers make sure the Applications Install Disc 2 is inserted into the built-in optical drive, external Apple Superdrive, or for the MacBook Air (Late 2010) be sure the MacBook Air Software Reinstall Drive is inserted into a USB port. Then, follow steps 1-6 outlined in the previous section of this article.