Fri Dec 19 . . . 2 1 emissary.edgenuity.com 2020.geniussis.com/FEDashboard.aspx e2020.geniussis.com/FEDashboard.aspx AP Calculus AB A - Imagine Edgenuity for St... x emissary.edgenuity.com/https://media. 1. Project: Optimizing at a Water-Treatment Plant 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 f(t) = 100 + 30cos-,, 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 g(t) = 30e cos(t/2). a) Define a new function, A'(t), that would represent the amount of untreated water inside the plant, at any given time, t. b) Find A' (t). 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. Copyright @ 2022 Imagine Learning LLC