15 - 17 Box open at the top in maxima and minima

Problem 15
A box is to be made of a piece of cardboard 9 inches square by cutting equal squares out of the corners and turning up the sides. Find the volume of the largest box that can be made in this way.
 

12 - 14 Rectangular Lot Problems in Maxima and Minima

Problem 12
A rectangular field of fixed area is to be enclosed and divided into three lots by parallels to one of the sides. What should be the relative dimensions of the field to make the amount of fencing minimum?

05 - 08 Number Problems in Maxima and Minima

Problem 5
The sum of two positive numbers is 2. Find the smallest value possible for the sum of the cube of one number and the square of the other.

Solution 5