A drinking cup is made in the shape of a right circular cylinder. for a fixed volume v0 we wish to make the total material used for the circular bottom and the cylindrical side as small as possible. use caclculus to determine the ration of the hight h to the diameter d unter the conditions stated in the problem

a) find the equation to maximized or minimized.
b) find the solution
c) showing that your solution is an absolute max or min.

Titus works at a hotel. part of his job is to keep the complimentary pitcher of water at least half full and always with ice. when he starts his shift, the water level shows 4 gallons, or 128 cups of water. as the shift progresses, he records the level of the water every 10 minutes. after 2 hours, he uses a regression calculator to compute an equation for the decrease in water. his equation is w –0.414t + 129.549, where t is the number of minutes and w is the level of water. according to the equation, after about how many minutes would the water level be less than or equal to 64 cups?