Detailed Table of Contents for Applied Calculus

Chapter 10 – Functions and Limits

Section 1 – Functions

Question 1 – What is a function?

Question 2 – What is function notation?

Question 3 – What is a piecewise defined function?

Section 2 – Basic Concepts of Limits

Question 1 – How do you evaluate a limit from a table?

Question 2 – How do you evaluate a limit from a graph?

Section 3 – Computing Limits Algebraically

Question 1 – How can a limit be computed algebraically?

Question 2 – How do you evaluate limits involving difference quotients?

Section 4 – Computing Limits at Infinity

Question 1 – How do you evaluate a limit at infinity using a table or graph?

Question 2 – How do you evaluate limits at infinity using algebra?

Section 5 – Continuous Functions

Question 1 – What does a continuous function look like?

Question 2 – How is a limit related to a continuous function?

Chapter 11 – Calculating Change

Section 1 – Average Rate of Change

Question 1 – How do you calculate the average rate of change from a table?

Question 2 – How do you calculate the average rate of change from a function?

Section 2 – Instantaneous Rate of Change

Question 1 – How do you estimate the instantaneous rate of change?

Question 2 – How do you compute the instantaneous rate of change using a limit?

Section 3 – The Derivative at a Point

Question 1 – What is a derivative?

Question 2 – How do you compute the derivative at a point using a limit?

Question 3 – How can you use a tangent line to forecast function values?

Question 4 – What does the derivative at a point tell you about a function?

Section 4 – The Derivative Function

Question 1 – What is a derivative function?

Question 2 – How do you calculate the derivative of a function from the definition?

Question 3 – What are the derivatives of some basic functions (linear, polynomial, power, exponential, and logarithmic)?

Section 5 – Economic Applications of the Derivative

Question 1 – What does the term marginal mean?

Question 2 – How are derivatives used to compute elasticity?

Section 6 – The Derivatives of Products and Quotients

Question 1 – How do you find the derivative of a product of two functions?

Question 2 – How do you find the derivative of a quotient of two functions?

Question 3 – What is an average cost function?

Section 7 – The Chain Rule

Question 1 – What is a composition of two functions?

Question 2 – How do you write a function as a composition of two functions?

Question 3 – How do you apply the chain rule to take a derivative?

Question 4 – How do you combine derivative rules to take more complicated derivatives?

Chapter 12 – Applying Derivatives

Section 1 – Extrema of a Function

Question 1 – What is the difference between a relative extremum and an absolute extremum?

Question 2 – What is a critical point of a function?

Question 3 – How do you find the relative extrema of a function?

Question 4 – How do you find the absolute extrema of a function?

Section 2 – Higher Derivatives

Question 1 – How is the second derivative calculated?

Question 2 – How are other higher derivatives calculated?

Question 3 – What does the second derivative of a function tell you about a function?

Question 4 – What is the point of diminishing returns?

Section 3 – Optimizing Business Functions

Question 1 – How do you maximize the revenue or profit for a business?

Question 2 – How do you minimize the average cost for a business?

Section 4 – Business Applications of Extrema

Question 1 – How do you find the optimal dimensions of a product?

Question 2 – How do we make decisions about inventory?

Chapter 13 – Calculating Area

Section 1 – Antiderivatives

Question 1 – What is an antiderivative?

Question 2 – What are the antiderivatives of some basic functions?

Question 3 – How do we find the antiderivative of functions that are combinations of basic functions?

Question 4 – How do we find the value of the arbitrary constant?

Section 2 – Approximating Area

Question 1 – Why is area important?

Question 2 – How is the area under a function approximated?

Section 3 – Definite Integral

Question 1 – What is a definite integral?

Question 2 – How is the definite integral related to the approximate area?

Section 4 – The Fundamental Theorem of Calculus

Question 1 – How do you calculate the total change of a quantity exactly?

Question 2 – What is the Fundamental Theorem of Calculus?

Chapter 14 – Integration Techniques

Section 1 – The Substitution Method

Question 1 – How do we find the antiderivative of functions involving compositions?

Question 2 – How is the exact area under a function involving compositions computed?

Question 3 – How do you undo a rate with the Substitution Method?

Section 2 – Integration by Parts

Question 1 – How do we find the antiderivative of functions involving products?

Question 2 – How is the exact area under a function involving products computed?

Section 3 – Area Between Curves

Question 1 – How is the area between two functions calculated?

Question 2 – What are consumers’ and producers’ surplus?

Chapter 15 – Multivariable Calculus

Section 1 – Functions of Several Variables

Question 1 – What is a function of two variables?

Question 2 – How do you graph a function of two variables?

Question 3 – What is the Cobb-Douglas production formula?

Section 2 – Partial Derivatives

Question 1 – How do you take a first partial derivative of a function?

Question 2 – What do the first partial derivatives of a function tell us?

Question 3 – How do you take the second partial derivative of a function?

Section 3 – Extrema of Multivariable Functions

Question 1 – What is a relative extrema and saddle point?

Question 2 – How do you find the relative extrema of a surface?

Section 4 – Constrained Maxima and Minima

Question 1 – How do you find the relative extrema of a surface when the values of the variables are constrained?

Question 2 – How do you model an optimization problem with several variables subject to a constraint?