Unformatted text preview: 12. A company would like to design a box (bottom, top and four sides), with square base using exactly 500 square inches of material, and having a height somewhere between 3 inches and 20 inches. How tall should the box be made so that its volume is as large as possible? 13. In inverted conical tank is draining water at a rate of 30 cubic centimeters per second. If the tank is 100 centimeters high and has a radius of 20 centimeters at the top, ﬁnd the rate at which the level of the water is falling when the level is at 30 centimeters. Reminder: the formula for the volume of a circular cone is V = 1 3 πr 2 h . 14. Consider the function f ( x ) = x + e x . Use Rolle’s theorem to show that there is at most one solution to the equation f ( x ) = 5. Hint: you may use the fact that e x > for all values of x ....
View
Full Document
 Spring '08
 CHESTKOFSKY
 Math, Calculus, Englishlanguage films, Imperial units, Inch

Click to edit the document details