# Maxima and Minima

## 58 - 59 Maxima and minima: cylinder surmounted by hemisphere and cylinder surmounted by cone

## 56 - 57 Maxima and minima problems of square box and silo

**Problem 56**

The base of a covered box is a square. The bottom and back are made of pine, the remainder of oak. If oak is m times as expensive as pine, find the most economical proportion.

## 53 - 55 Solved Problems in Maxima and Minima

**Problem 53**

Cut the largest possible rectangle from a circular quadrant, as shown in Fig. 40.

## 50 - 52 Nearest distance from a given point to a given curve

**Problem 50**

Find the shortest distance from the point (4, 2) to the ellipse x^{2} + 3y^{2} = 12.

## 48 - 49 Shortest distance from a point to a curve by maxima and minima

**Problem 48**

Find the shortest distance from the point (5, 0) to the curve 2y^{2} = x^{3}.

## 46 - 47 Solved Problems in Maxima and Minima

**Problem 46**

Given point on the conjugate axis of an equilateral hyperbola, find the shortest distance to the curve.

## 43 - 45 Solved problems in maxima and minima

**Problem 43**

A ship lies 6 miles from shore, and opposite a point 10 miles farther along the shore another ship lies 18 miles offshore. A boat from the first ship is to land a passenger and then proceed to the other ship. What is the least distance the boat can travel?

## 41 - 42 Maxima and Minima Problems Involving Trapezoidal Gutter

**Problem 41**

In Problem 39, if the strip is L in. wide, and the width across the top is T in. (T < L), what base width gives the maximum capacity?

## 38 - 40 Solved problems in maxima and minima

**Problem 38**

A cylindrical glass jar has a plastic top. If the plastic is half as expensive as glass, per unit area, find the most economical proportion of the jar.

## 35 - 37 Solved problems in maxima and minima

**Problem 35**

A page is to contain 24 sq. in. of print. The margins at top and bottom are 1.5 in., at the sides 1 in. Find the most economical dimensions of the page.