Prove inelastic collision loses the most KE?

[Chickensalad]

Homework Statement

Prove that inelastic collisions have the most KE loss of any type of collision (i.e. partially inelastic and elastic are the others)[/B]

Homework Equations

m₁v₁+ m₂v₂= (m₁+m₂)V_f

The Attempt at a Solution

I have solved for Vf in that V_f=(m₁v₁+m₂v₂)/(m₁+m₂), but I am totally unsure as to where to go from here [/B]

 

[haruspex]

If you want to show it retains the least energy out of all the possibilities, then you will need an equation that encompasses all possibilities. Start with a general equation for one dimensional collision and express the energy retained (or the energy lost, if you think that will be more helpful) in terms of the final velocities.
You will then want to get it in terms of a single variable somehow related to the final velocities. Consider what relationship you are trying to establish, and what single function of the two would encapsulate that relationship.