# Maxima and Minima

## 32 - 34 Maxima and minima problems of a rectangle inscribed in a triangle

## 29 - 31 Solved problems in maxima and minima

**Problem 29**

The sum of the length and girth of a container of square cross section is a inches. Find the maximum volume.

## 28 - Solved problem in maxima and minima

**Problem 28**

The perimeter of an isosceles triangle is P inches. Find the maximum area.

## 25 - 27 Solved problems in maxima and minima

**Problem 25**

Find the most economical proportions of a quart can.

## 21 - 24 Solved problems in maxima and minima

**Problem 21**

Find the rectangle of maximum perimeter inscribed in a given circle.

## 18 - 20 Rectangular beam in maxima and minima problems

**Problem 18**

The strength of a rectangular beam is proportional to the breadth and the square of the depth. Find the shape of the largest beam that can be cut from a log of given size.

## 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?

## 09 - 11 Rectangular Lot Problems in Maxima and Minima

**Problem 9**

What should be the shape of a rectangular field of a given area, if it is to be enclosed by the least amount of fencing?

## 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**