 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 ladder—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 problem—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 279375 students have viewed full stepbystep solutions from this chapter. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567.

Base
See Exponential function, Logarithmic function, nth power of a.

Coefficient matrix
A matrix whose elements are the coefficients in a system of linear equations

Completing the square
A method of adding a constant to an expression in order to form a perfect square

Components of a vector
See Component form of a vector.

Constant function (on an interval)
ƒ(x 1) = ƒ(x 2) x for any x1 and x2 (in the interval)

Dependent variable
Variable representing the range value of a function (usually y)

Empty set
A set with no elements

Equivalent equations (inequalities)
Equations (inequalities) that have the same solutions.

Focal width of a parabola
The length of the chord through the focus and perpendicular to the axis.

Index
See Radical.

Logistic regression
A procedure for fitting a logistic curve to a set of data

Midpoint (in Cartesian space)
For the line segment with endpoints (x 1, y1, z 1) and (x2, y2, z2), ax 1 + x 22 ,y1 + y22 ,z 1 + z 22 b

Obtuse triangle
A triangle in which one angle is greater than 90°.

Parallel lines
Two lines that are both vertical or have equal slopes.

Parametric curve
The graph of parametric equations.

Pseudorandom numbers
Computergenerated numbers that can be used to approximate true randomness in scientific studies. Since they depend on iterative computer algorithms, they are not truly random

Slant asymptote
An end behavior asymptote that is a slant line

Solve by substitution
Method for solving systems of linear equations.

Synthetic division
A procedure used to divide a polynomial by a linear factor, x  a

Triangular number
A number that is a sum of the arithmetic series 1 + 2 + 3 + ... + n for some natural number n.