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# Solutions for Chapter 4.7: Optimization Problems

## Full solutions for Single Variable Calculus: Early Transcendentals | 8th Edition

ISBN: 9781305270336

Solutions for Chapter 4.7: Optimization Problems

Solutions for Chapter 4.7
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##### ISBN: 9781305270336

Single Variable Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781305270336. This textbook survival guide was created for the textbook: Single Variable Calculus: Early Transcendentals, edition: 8. Since 82 problems in chapter 4.7: Optimization Problems have been answered, more than 107079 students have viewed full step-by-step solutions from this chapter. Chapter 4.7: Optimization Problems includes 82 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions.

Key Calculus Terms and definitions covered in this textbook
• Arccosecant function

See Inverse cosecant function.

• Cofunction identity

An identity that relates the sine, secant, or tangent to the cosine, cosecant, or cotangent, respectively

• Cone

See Right circular cone.

• De Moivre’s theorem

(r(cos ? + i sin ?))n = r n (cos n? + i sin n?)

• Domain of a function

The set of all input values for a function

• Heron’s formula

The area of ¢ABC with semiperimeter s is given by 2s1s - a21s - b21s - c2.

• Histogram

A graph that visually represents the information in a frequency table using rectangular areas proportional to the frequencies.

• Inverse variation

See Power function.

• Mathematical induction

A process for proving that a statement is true for all natural numbers n by showing that it is true for n = 1 (the anchor) and that, if it is true for n = k, then it must be true for n = k + 1 (the inductive step)

• One-to-one function

A function in which each element of the range corresponds to exactly one element in the domain

• Orthogonal vectors

Two vectors u and v with u x v = 0.

• Pseudo-random numbers

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

• Right triangle

A triangle with a 90° angle.

• Row operations

See Elementary row operations.

• Scatter plot

A plot of all the ordered pairs of a two-variable data set on a coordinate plane.

• Standard representation of a vector

A representative arrow with its initial point at the origin

• Symmetric matrix

A matrix A = [aij] with the property aij = aji for all i and j

• Triangular form

A special form for a system of linear equations that facilitates finding the solution.

• Vertical line test

A test for determining whether a graph is a function.

• Whole numbers

The numbers 0, 1, 2, 3, ... .