4ObjectiveTo form a function of one variable from a verbal description and, when appropriate, to determine the minimum or maximum value of the function.
5A box with a square base and top has a volume of 10 meters cubed. The materialfor the base costs $12 per square meterand the material for the sides costs $8 persquare meter. Express the cost C of thematerial as a function of the width.
6Water flows into a conical tank 100 cm wide and 250 cm deep at a rate of40 cubic centimeters per second. Findthe volume in terms of the height of thetank and the height in terms of the time.
7Water is flowing into a cylindrical tank at 6 cubic meters per second. The radiusis 20 meters and the height of the tank is100 meters. Find the volume in terms ofthe height of the tank and the height interms of the time.
8P(x,y) is an arbitrary point on the parabola y = x2 P(x,y) is an arbitrary point on the parabola y = x2. Express the distance, d, from P to the point A (2,1) as a function of the x-coordinate of P.
9Ticket to leave:A cylinder with no top has a volume of 20 m3. Express the total surface area of the box as a function of the radius, r, of the base.