 4.4.1E: Fill in the blanks: The goal of an optimization problem is to find ...
 4.4.2E: If the objective function involves more than one independent variab...
 4.4.3E: 2 If the objective functio ? n is ?Q = x y ? and you know? tha? t? ...
 4.4.4E: Suppose you wish to minimize a continuous objective function on a c...
 4.4.5E: Maximum area rectangles Of all rectangles with a perimeter of 10 m,...
 4.4.6E: Minimum perimeter rectangles Of all rectangles with a fixed area A,...
 4.4.7E: Maximum product What two nonnegative real numbers with a sum of 23 ...
 4.4.8E: Maximum length What two nonnegative real numb ? ers? ? nd ? whose s...
 4.4.9E: Minimum sum What two positive real numbers whose product is 50 have...
 4.4.10E: Pen problems a. A rectangular pen is built with one side against a ...
 4.4.11E: Minimum surface area box of all boxes with a square base and a volu...
 4.4.12E: Maximum volume box Suppose an airline policy states that all baggag...
 4.4.13E: Shipping crates A squarebased, boxshaped shipping crate is design...
 4.4.14E: Walking and swimming A man wishes to gel from an initial point on t...
 4.4.15E: Walking and rowing A boat on the ocean is 4 mi from the nearest poi...
 4.4.16E: Shortest ladder A 10fttall fence runs parallel to the wall of a h...
 4.4.17E: Shortest ladderâ€”more realistic An 8fttall fence runs parallel to ...
 4.4.18E: Rectangles beneath a parabola A rectangle is constructed with its b...
 4.4.19E: Rectangles beneath a semi circle A rectangle is constructed with it...
 4.4.20E: Circle and square A piece of wire 60 cm in length is cut, and the r...
 4.4.21E: Maximum volume cone A cone is constructed by cutting a sector of an...
 4.4.22E: Covering a marble Imagine a flatbottomed cylindrical pot with a ci...
 4.4.23E: 2 Optimal garden A rectangular flower garden with an area of 30 m i...
 4.4.24E: rectangles beneath a line a. A rectangle is constructed with one si...
 4.4.25E: Kepler's wine barrel Several mathematical stories originated with t...
 4.4.26E: Folded boxes (a). Squares with sides of ?length x ? are cut out of ...
 4.4.27E: Making silos A grain silo consists of a cylindrical concrete tower ...
 4.4.39E: Optimal soda can a. Classical problem Find the radius and height of...
 4.4.40E: Cylinder and cones (Putnam Exam 1938) Right circular cones of he ? ...
 4.4.41E: Viewing angles An auditorium with a flat floor has a large screen o...
 4.4.42E: Searchlight problemâ€”narrow beam A searchlight is 100 in from the ne...
 4.4.43E: Watching a Ferris wheel An observer stands 20 m from the hot tom of...
 4.4.44E: Maximum angle Find the valu?e of x? that maxim?izes ? in the figure.
 4.4.45E: Maximum volume cylinder in a sphere Find the dimensions of the righ...
 4.4.46E: Rectangles in triangles Find the dimensions and area of the rectang...
 4.4.47E: Cylinder in a cone A right circular cylinder is placed inside a con...
 4.4.48E: Maximizing profit Suppose you own a tour bus and you book groups of...
 4.4.49E: Come in a cone A right circular cone is inscribed inside a larger r...
 4.4.50E: Another pen problem A rancher is building a horse pen on the corner...
 4.4.51E: Minimumlength roads A house is located at each corner of a square ...
 4.4.52E: Light transmission A window consists of a rectangular pane of clear...
 4.4.53E: Slowest shortcut Suppose you are standing in a field near a straigh...
 4.4.54E: The arbelos An arbelos is the region enclosed by three mutually tan...
 4.4.55E: Proximity questions a. What point on the line y ? ? = ? ? + 4 is cl...
 4.4.56E: Turning a corner with a pole a. What is the length of the longest p...
 4.4.57E: Travel costs A simple model for travel costs involves the cost of g...
 4.4.58E: Do dogs know calculus? A mathematician stands on a beach with his d...
 4.4.59E: Fermat's Principle a. Two poles of he? ights ?? and n? are separate...
 4.4.60E: Snell's Law Suppose that a light sourc ? e at? is in a medium in wh...
 4.4.61E: Tree notch (Putnam Exam 1938, rephrased) A notch is cut in a cylind...
 4.4.62E: Gliding mammals Many species of small mammals (such as flying squir...
Solutions for Chapter 4.4: Calculus: Early Transcendentals 1st Edition
Full solutions for Calculus: Early Transcendentals  1st Edition
ISBN: 9780321570567
Solutions for Chapter 4.4
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 4.4 includes 51 full stepbystep solutions. Since 51 problems in chapter 4.4 have been answered, more than 83063 students have viewed full stepbystep solutions from this chapter. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567.

Addition property of inequality
If u < v , then u + w < v + w

Blind experiment
An experiment in which subjects do not know if they have been given an active treatment or a placebo

Closed interval
An interval that includes its endpoints

Compounded monthly
See Compounded k times per year.

Constant term
See Polynomial function

Division
a b = aa 1 b b, b Z 0

Fibonacci sequence
The sequence 1, 1, 2, 3, 5, 8, 13, . . ..

Focus, foci
See Ellipse, Hyperbola, Parabola.

Infinite sequence
A function whose domain is the set of all natural numbers.

Inverse secant function
The function y = sec1 x

Measure of spread
A measure that tells how widely distributed data are.

Parameter
See Parametric equations.

Partial fraction decomposition
See Partial fractions.

Polar equation
An equation in r and ?.

Pythagorean identities
sin2 u + cos2 u = 1, 1 + tan2 u = sec2 u, and 1 + cot2 u = csc2 u

Reference triangle
For an angle ? in standard position, a reference triangle is a triangle formed by the terminal side of angle ?, the xaxis, and a perpendicular dropped from a point on the terminal side to the xaxis. The angle in a reference triangle at the origin is the reference angle

Semiminor axis
The distance from the center of an ellipse to a point on the ellipse along a line perpendicular to the major axis.

Simple harmonic motion
Motion described by d = a sin wt or d = a cos wt

Solution of an equation or inequality
A value of the variable (or values of the variables) for which the equation or inequality is true

yaxis
Usually the vertical coordinate line in a Cartesian coordinate system with positive direction up, pp. 12, 629.