E6440 laptop CPU upgrade

You will face issues.  The system never shipped with Extreme Edition CPUs, so:

1.  The system may not even pass POST with an unsupported CPU aboard,

2.   If the system does POST, it may not run for long - or in stable fashion -- with the MX CPU, which draws 20W more (and therefore produces a concomitantly greater heat output) than the original CPU.  That's over 50% more power draw than the supported CPU this system is designed to handle.

3.  The heat issue will cause the system to throttle, meaning the MX CPU will almost certainly perform slower than the CPU you now have, as the system will throttle back to reduce the heat load.  Plenty of test out there with modern systems show that the i9 version actually runs slower in the real world than the i7 for exactly the same reason.

Unless you're in this for an experiment that will more likely fail than succeed, it's not worth the attempt.  The CPUs cost anwhere north of $150 as a used part -- or about what the entire value of the system is at this point, perhaps more.

If you're looking for better performance, or want that CPU, look for a used system with it -- which will be a large-footprint gaming or workstation class system with the space to contain a heatsink and multiple fans necessary to keep it running in specification. 

do you know the absolute strongest cpu i can install in it? that would run without much problems