It's also about time we had a Canon 1.4x and 2.0x extender that retained AF past f5.6/8.0 - I'm sure it's a marketing ploy rather than technical
Haydn1971, meet optical physics. Optical physics, meet Haydn1971. It's clear the two don't know each other.
The f/number is a ratio of focal length to the diameter of the iris diaphragm. Putting the TC behind the lens increases the focal length, but doesn't change the physical aperture inside the lens.
A 400mm f/5.6 lens has a 71.4mm physical aperture: 400mm/71.4mm = 5.6. If you put a 1.4x TC behind it, you multiply the focal length by 1.4x, to 560mm. Therefore, you now have a 560mm/71.4mm = f/7.84 (call it f/8) lens. If your camera supports AF at only f/5.6, AF won't work.
A 200mm f/2 lens has a 100mm physical aperture: 200mm/100mm = 2. If you put a 2x TC behind it, you multiply the focal length by 2x, to 400mm. Therefore, you now have a 400mm/100mm = f/4 lens.