Imagine you are an engineer for a water-treatment plant, and you must determine the optimal amount of water in the plant over a 24-hour period. On a particular day, the amount of untreated water coming into the plant can be modeled by ????(????) = 100 + 30cos ????/6 ,, where t is in hours since midnight and f(t) represents thousands of gallons of water. The amount of treated water at any given time, t, can be modeled by ????(????) = 30???? cos(????/2) .

a) Define a new function, ????′(????), that would represent the amount of untreated water inside the plant, at any given time, t.

b) Find ???? ′ (????).

c) Determine the critical values of this function over the interval [0, 24).

d) Determine whether the critical values represent local maximums or minimums.

e) Determine the maximum and minimum amount of untreated water in the plant for the day.

Answer rating: 100% (QA)

a The new function for the amount of untreated water inside the plant at any given time t is ut ft g... View the full answer