Why do production functions, or total product curves, most often change their slope over varied input levels?

Answer 1

Because different combinations of input allow different levels of output to be made.  Also (and probably more technically correct) because of the diminishing marginal returns of inputs beyond a certain level of input.  

Imagine you have two inputs, nails and wood.  If you have only wood, you could probably make a couple things, if you were really skilled with a saw and could fit the wood together perfectly.  If you have only nails, you might could make one of those neat puzzles where you have to separate the bent together nails, or maybe some kind of weird metal sculpture... but you wouldn't be able to make a lot.

Now if you vary the levels of nails and wood to some points in between, you could make all sorts of stuff.  if you have a lot of nails and a little wood, you could maybe make ... i dunno, anything that takes a lot of fasteners (haha!) ... if you have a lot of wood and only a few nails, maybe you could make anything that is large but doesn't have that many places you need nails.  

OK so maybe that wasn't the greatest example.  But you could think of it with any two inputs -- money and workers, spaghetti and meat sauce, any two.  And at some point there is going to usually be a maximum and a minimum level of production also.  

Sorry my example was lame but I hope this helped you understand the concept you are asking about.