Newer more advanced operating systems and other software are more demanding of the hardware in your system. Some slowdown is expected.
How full is your hard drive? If you've got less than 10% of the capacity remaining, that could be your problem.
Have you tried reformatting the HDD and installing a fresh copy of OSX? Don't restore from your backup, as that can restore software issues that are causing the problems in the first place. Normally I wouldn't go this route, but if you've done several OS upgrades since you bought the computer in 2011, it may be warranted.
If you plan on keeping the computer for a while and a fresh install of OSX doesn't help, you may want to look into upgrading to a SSD. Most of the time they will breathe new life into an older system.