How do I update my Facebook app on my iPad mini

If there is an update available for the app that's compatible with your iPad's iOS version it should show in the Purchased tab in the App Store app for downloading

Open the App Store app and tap Updates at lower right.

If you want to update apps automatically, refer to this link: Turn on Automatic Downloads for iTunes Store, App Store, and iBooks Store purchases - Apple Support

But if you want to update it manually,

1. Open App Store
2. Tap Updates at bottom right
3. And if Facebook's update is available, tap Update.