So now we're ready to answer, at what time t is the amount of water in the pipe at a minimum? We can see that at time 3.272, we have less water in the pipe than either right when we started or right at the end of our interval at t equals eight. So at what time t? We say t is equal to 3.272. We could write w of 3.272 is less than w of zero, which is less than w of eight. So this indeed, just by knowing that the derivative there is zero, it could be a minimum or a maximum, but the fact that it's lower than both of the endpoints, this tells us that hey, this is a minimum, minimum, minimum point right over there. Or we could say that t equals 3.272 is where we hit our minimum, minimum value.