Water is flowing into and out of two vats, Vat A and Vat B. The amount of water, in gallons, in Vat A at time t hours is given by a function A(t) and the amount in Vat B is given by B(t). The two vats contain the same amount of water at t=0. You have a formula for the rate of flow for Vat A and the amount in Vat B: Vat A rate of flow: A(t)-3t2+24t-21 Vat B amount: B(t)-2t2+16t+40 (a) Find all times at which the graph of A(t) has a horizontal tangent and determine whether each gives a local maximum or a local minimum of A(t) smaller t= 1 gives a local minimum larger t= 7 l maximum
(b) Let D(t)-B(t)-A(t). Determine all times at which D(t) has a horizontal tangent and determine whether each gives a local maximum or a local minimum. (Round your times to two digits after the decimal.) xgives a Select x gives a Select smaller t- larger t=
(c) Use the fact trruntain the same amount of water at ta0 to find the formula for A(), the amount in Vat A at time t Enter a number
(d) At what time is the water level in Vat A rising most rapidly? t- hours
(e) what is the highest water level in Vat A during the interval from t=0 to t=10 hours? gallons
(f) What is the highest rate at which water flows into Vat B during the interval from t-0 to t-10 hours? gallons per hour
(g) How much water flows into VatA during the interval from t=1 to t-8 hours? gallons