Latest Kernel for ubuntu 14.04.4

Solution 1:

You do not have to upgrade your kernel. Kernel 3.16 still gets security and bug fixing updates.

But you CAN upgrade the kernel to 3.19 by

sudo apt-get install linux-generic-lts-vivid

or to 4.2 by

sudo apt-get install linux-generic-lts-wily

It is even possible to upgrade to kernel 4.4, but that may cause issues with DKMS modules

sudo apt-get install linux-generic-lts-xenial