Differential Calculus

Maxima/Minima Problems L A rectangular eld Is to be fenced off along a straight river. If no fencing is needed along 9'" 5. the river, show that the least amount of fencing will be required when the length of the eld is twice its width. Find the shape of the largest rectangle that can be inscribed in a given circle. Divide the number 60 into two parts so that the product P of one part and the square of the other is maximum. What is the maximum volume of a box that Is constructed from a piece of cardboard 16 inches square by cutting equal squares out of the comers and turning up the sides? A square sheet of galvanized iron. 100 cm x 100 cm will be used in making an open top container by cutting a small square from each corner and bending up the sides. Determine how large the square should be cut from each corner in order to obtain the largest possible volume