Homework Help: Always a minimum

1. Mar 7, 2010

aznwei

1. The problem statement, all variables and given/known data

For a ball thrown up in the air show that the stationary value of the action is always a global minimum

2. Relevant equations

euler lagrange equation and action equation(sorry i don't know syntax here)

3. The attempt at a solution
well basically here i used the euler lagrange equation where L=T-V and by using the principle of stationary action figured out that a=g.....by solving the differential equation i found a equaiton of motion for y(t). Thus i sub this into the action equation of S=integral(L)dt and integrate it getting the answer mg^2t^3/6+g^2T^3/2 . and this is where i'm stuck ......i don't know how to show whether this is a global minimum or nor not and also if even my initial steps are correct. If someone could please point me in the right direction it would be great. Thanks.