Update Linux Kernel on Mint or Ubuntu

for upgrade you need three packages, depending on you architecture:

linux-headers ... ... ... amd64.deb
linux-headers ... ... ... all.deb
linux-image   ... ... ... amd64.deb

if you use Ubuntu based Linux distro, you can pick one of these: 

http://kernel.ubuntu.com/~kernel-ppa/mainline/

for example:

$ cd /tmp 

$ wget http://kernel.ubuntu.com/~kernel-ppa/mainline/v4.0.1-vivid/linux-headers-4.0.1-040001-generic_4.0.1-040001.201504290935_amd64.deb

$ wget http://kernel.ubuntu.com/~kernel-ppa/mainline/v4.0.1-vivid/linux-headers-4.0.1-040001_4.0.1-040001.201504290935_all.deb

$ wget http://kernel.ubuntu.com/~kernel-ppa/mainline/v4.0.1-vivid/linux-image-4.0.1-040001-generic_4.0.1-040001.201504290935_amd64.deb

$ sudo dpkg -i *.deb

$ sudo update-grub

If for some reason you want to downgrade the kernel, it loads the newest kernel by default, so just uninstall new one (three packages that I mentioned) and it will load second on the list after reboot. Make sure you have at least one kernel installed! :)