## anonymous 5 years ago On a certain day the temperature t hours past midnight was T(t)=60+5sin((pi/6)(t-10)). What was the average temperature between noon and mignight of the same day? I know that you would use the mean value theorem for integrals to solve this which I know how, but why?

1. anonymous

Wouldn't you just use the mean value thoerem for derivatives since you're trying to find the average temperature? Not time*temperature as the area under the curve of this function suggests?

2. anonymous

you're right we are looking for average temperature and we are looking at area under curve but not of T but T' _>$=1/12\int\limits_{0}^{12}T 'dt$ which really is (T(12)-T(0))/12

3. anonymous

think of it as Temp/time * time