 3.R.1E: What is the derivative of a function ƒ? How is its domain related t...
 3.R.2E: What role does the derivative play in defining slopes, tangents, an...
 3.R.3E: How can you sometimes graph the derivative of a function when all y...
 3.R.4E: What does it mean for a function to be differentiable on an open in...
 3.R.5E: How are derivatives and onesided derivatives related?
 3.R.6E: Describe geometrically when a function typically does not have a de...
 3.R.7E: How is a function’s differentiability at a point related to its con...
 3.R.8E: What rules do you know for calculating derivatives? Give some examp...
 3.R.9E: Explain how the three formulas enable us to differentiate any polyn...
 3.R.10E: What formula do we need, in addition to the three listed in Questio...
 3.R.11E: What is a second derivative? A third derivative? How many derivativ...
 3.R.12E: What is the derivative of the exponential function ex? How does the...
 3.R.13E: What is the relationship between a function’s average and instantan...
 3.R.14E: How do derivatives arise in the study of motion? What can you learn...
 3.R.15E: How can derivatives arise in economics?
 3.R.16E: Give examples of still other applications of derivatives.
 3.R.17E: What do the limits and have to do with the derivatives of the sine ...
 3.R.18E: Once you know the derivatives of sin x and cos x, how can you find ...
 3.R.19E: At what points are the six basic trigonometric functions continuous...
 3.R.20E: What is the rule for calculating the derivative of a composite of t...
 3.R.21E: If u is a differentiable function of x, how do you find (d/dx)(un) ...
 3.R.22E: What is implicit differentiation? When do you need it? Give examples.
 3.R.23E: What is the derivative of the natural logarithm function ln x? How ...
 3.R.24E: What is the derivative of the exponential function ax and a > 0 and...
 3.R.25E: What is the derivative of loga x? Are there any restrictions on a?
 3.R.26E: What is logarithmic differentiation? Give an example.
 3.R.27E: How can you write any real power of x as a power of e? Are there an...
 3.R.28E: What is one way of expressing the special number e as a limit? What...
 3.R.29E: What are the derivatives of the inverse trigonometric functions? Ho...
 3.R.30E: How do related rates problems arise? Give examples.
 3.R.31E: Outline a strategy for solving related rates problems. Illustrate w...
 3.R.32E: What is the linearization L(x) of a function ƒ(x) at a point x = a?...
 3.R.33E: If x moves from a to a nearby value a + dx, how do you estimate the...
Solutions for Chapter 3.R: University Calculus: Early Transcendentals 2nd Edition
Full solutions for University Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321717399
Solutions for Chapter 3.R
Get Full SolutionsSince 33 problems in chapter 3.R have been answered, more than 55288 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: University Calculus: Early Transcendentals , edition: 2. Chapter 3.R includes 33 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. University Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321717399.

Bar chart
A rectangular graphical display of categorical data.

Central angle
An angle whose vertex is the center of a circle

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

Common difference
See Arithmetic sequence.

Compound fraction
A fractional expression in which the numerator or denominator may contain fractions

Convergence of a sequence
A sequence {an} converges to a if limn: q an = a

Directed angle
See Polar coordinates.

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

Inverse tangent function
The function y = tan1 x

Linear equation in x
An equation that can be written in the form ax + b = 0, where a and b are real numbers and a Z 0

Local maximum
A value ƒ(c) is a local maximum of ƒ if there is an open interval I containing c such that ƒ(x) < ƒ(c) for all values of x in I

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

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

Multiplication property of equality
If u = v and w = z, then uw = vz

Objective function
See Linear programming problem.

Polynomial function
A function in which ƒ(x)is a polynomial in x, p. 158.

Probability function
A function P that assigns a real number to each outcome O in a sample space satisfying: 0 … P1O2 … 1, P12 = 0, and the sum of the probabilities of all outcomes is 1.

Standard form of a polynomial function
ƒ(x) = an x n + an1x n1 + Á + a1x + a0

Supply curve
p = ƒ(x), where x represents production and p represents price

Tangent
The function y = tan x