I'm often asked to send clips with handles to other editors that I'm working with. Final Cut Pro X somehow still doesn't support exporting a clip with handles directly from the timeline, which hopefully will be fixed soon.
Until then, I've been using a method that can "Resolve" this problem!
THE STEP BY STEP
Complete your edit as you would normally, export the project FCPXML from Final Cut Pro X.
Fire up DaVinci Resolve and import that FCPXML by going to FILE>IMPORT AAF/EDL/XML from the top menu bar.
This will prompt you with some settings windows, just click OK.
Now your timeline should be open in Resolve. In the edit page you can select the clips you'd like to export with handles most easily by using markers.
Once you've marked your clips you want to export with handles, you can go to the Export page and select the "Clips" drop down menu to filter for the clips with markers. Make sure to set your Export Destination and choose "Individual Clips".
Choose the codec, resolution, etc that you want to export the clip(s) as, and at the very bottom of the "Advanced" drop down tab you can choose to add your desired length of handles. Once you do this, add the job to the render queue and export as normal.
Your selected clips will be exported with handles, easy as that.
Please go here and ask Apple to implement this much needed feature: http://www.apple.com/feedback/finalcutpro.html