I'd use Chrome browser's built in Dev Tools to start off. cURL is not suitable for this because you cannot conveniently investigate individual file response times and have a good overview at your disposal.
Ctrl + Shift + i
to open, and navigate to Network tab. Then visit the web site reported slow and see how long it takes for the entire page to load. Then repeat and visit the web site bypassing F5 - for that you type in end-server's internal IP address or DNS name. See if there's any considerable difference between the two (value of
Finish
time). Also note if any individual files make up 50% or more of entire load time. This should be noted and discussed further with application specialists. Usually slowness issues can be solved or alleviated with the use of compression and caching features. Both can be applied in BigIP LTM.
If there are no signs of slowness in your tests, there are some client-specific issues that could play a role. Things like customers geographic location, or presence of 2G or 3G mobile internet.