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# Solutions for Chapter 4: USING THE DERIVATIVE

## Full solutions for Calculus: Single and Multivariable | 6th Edition

ISBN: 9780470888612

Solutions for Chapter 4: USING THE DERIVATIVE

Solutions for Chapter 4
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##### ISBN: 9780470888612

This textbook survival guide was created for the textbook: Calculus: Single and Multivariable , edition: 6. Since 108 problems in chapter 4: USING THE DERIVATIVE have been answered, more than 43291 students have viewed full step-by-step solutions from this chapter. Chapter 4: USING THE DERIVATIVE includes 108 full step-by-step solutions. Calculus: Single and Multivariable was written by and is associated to the ISBN: 9780470888612. This expansive textbook survival guide covers the following chapters and their solutions.

Key Calculus Terms and definitions covered in this textbook
• artesian coordinate system

An association between the points in a plane and ordered pairs of real numbers; or an association between the points in three-dimensional space and ordered triples of real numbers

• Bounded above

A function is bounded above if there is a number B such that ƒ(x) ? B for all x in the domain of ƒ.

• Characteristic polynomial of a square matrix A

det(xIn - A), where A is an n x n matrix

• Compounded continuously

Interest compounded using the formula A = Pert

• Demand curve

p = g(x), where x represents demand and p represents price

• Equally likely outcomes

Outcomes of an experiment that have the same probability of occurring.

• Extracting square roots

A method for solving equations in the form x 2 = k.

• Factored form

The left side of u(v + w) = uv + uw.

• Inverse function

The inverse relation of a one-to-one function.

• Inverse of a matrix

The inverse of a square matrix A, if it exists, is a matrix B, such that AB = BA = I , where I is an identity matrix.

• Lemniscate

A graph of a polar equation of the form r2 = a2 sin 2u or r 2 = a2 cos 2u.

• Nappe

See Right circular cone.

• Partial sums

See Sequence of partial sums.

• Polar form of a complex number

See Trigonometric form of a complex number.

• Present value of an annuity T

he net amount of your money put into an annuity.

• Resolving a vector

Finding the horizontal and vertical components of a vector.

• Secant line of ƒ

A line joining two points of the graph of ƒ.

• Sum of a finite arithmetic series

Sn = na a1 + a2 2 b = n 2 32a1 + 1n - 12d4,

• Term of a polynomial (function)

An expression of the form anxn in a polynomial (function).

• Zero factor property

If ab = 0 , then either a = 0 or b = 0.

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