Hello and welcome to my User Tip
There are some possible causes why your Mac is now slow after upgrading to OS X Mavericks.
1: If you have a boot hard drive (not a Solid State Drive) , their read/write performance degrades the more they are filled up, especially past the 50% point on the drive.
Backup and reduce users files on the machine to a external storage drive (not only TimeMachine), clone and reverse clone what is remaining using another drive and cloning software. Defrags and optimizes, will not fix issues in OS X, just clones the bad and the good.
2: If you have a boot hard drive (not a SSD), it's possible when Mavericks was written to the drive, it was done so on bad/failing sectors previously unused before and tested by the driver firmware for bit rot and switched out for a spare sector. (see a spinning beach ball effect)
Backup your users files immediately to external storage drives and be sure to 0-3x secure erase the hard drive, reinstall OS X.
Fixes all possible issues in OS X. See A 1-3 here, . Reset your Mac
3: It's possible the Mavericks upgrade didn't install correctly or completely. One can resinstall OS X over itself to fix it. Will not optimize/defrag OS X though like the above 1-2 will.
See #8 here. ..Step by Step to fix your Mac
4: You just upgraded from Snow Leopard, which is a slimmer, optimized OS X version for 32 bit processors and their 3.5GB RAM limit (but also runs on 64bit) and now transitioned to a full 64bit OS X (10.7-10.9) and it's unlimited RAM access, thus it and it's software is more feature rich for the more recent hardware.
It's possible to revert back to Snow Leopard, 10.7 or 10.8 using this user tip, provided it hasn't been too long as your files get changed by the newer software.
Not easy and there is a chance of risk the longer your on a later OS X version.
5: Your Mac is older than a Early 2011 model, which many report a noticeable decrease in performance for older machines.
6: Your Mac doesn't have enough RAM, 4GB minimal (Apple says 2GB), 8-16GB is more preferred because like mentioned, everyone is bloating their code (like Chrome is) to take advantage of the more RAM to do more things and run faster as RAM is even faster than SSD's in performance.
7: You have a third party (non-Apple) installed SSD and need to re-enable TRIM support using your third party software.
8: You might have a failing boot hard drive or other Mac or external hardware issue. Take it into Apple for a free check.
9: Mavericks might be having conflicts with your third party software, contact the developer and see if others report the same issues on their forums.
10: There might be other issues, for more details, read my User Tip here: Why is my computer slow?
Will add more if there are any Maverick specific issues appearing or being reported.