### Math 102 - Calculus I with Economics Applications Reading Assignments - September 2003

Be sure to check back, because this may change during the semester.

I'll use Maple syntax for mathematical notation on this page. All numbers indicate sections from Calculus from Graphical, Numerical, and Symbolic Points of View, Second Edition by Ostebee/Zorn.

### For Friday September 5

Section 1.1 Functions, Calculus Style
Section 1.2 Graphs

To read : The Section How to Use This Book: Notes for Students beginning on page xvii. All of Sections 1.1 and 1.2.

1. How is the graph of y=f(x)+3 =x2+3 related to the graph of y=f(x)? Why?
2. How is the graph of y=f(x+3) =(x+3)2 related to the graph of y=f(x)? Why?
3. Which of f(x), f(x)+2, and f(x+2) are even? odd?

### For Monday September 8

Section 1.3 A Field Guide to Elementary Functions

To read : All. Be sure to understand the definition of the logarithm function base b and the definitions of sin(x) and cos(x) in terms of the unit circle.

1. How are the functions f(x)=3x and g(x)=log3(x) related?
2. What are some of the main properties of sin(x)?

### For Wednesday September 10

Section 1.4 Amount Functions and Rate Functions: The Idea of the Derivative

To read : Through Example 4. Be sure understand the section "Rates, amounts, and cars" beginning on page 36.

Reading Questions : Look at the graphs of P(t) and V(t) in Figure 1 on page 37.
1. Is the derivative of P positive or negative at t=5 ? Explain.
2. Is the second derivative of P positive or negative at t=5 ? Explain.
3. Give a value of t where the derivative of P is zero.

### For Friday September 12

Section 1.5 Estimating Derivatives: A Closer Look

To read : All. Make sure to understand Examples 3 and 4.

1. What does the term "locally linear" mean?
2. Explain why the derivative of f(x)=|x| does not exist at x=0.

### For Monday September 15

Section 1.6 The Geometry of Derivatives

To read : All. Be sure to understand the definition of a stationary point and the difference between local and global maxima and minima.

Reading Questions : Look at the graph of f ' in Example 2:
1. Where does f have stationary points? Why?
2. Where is f increasing? Why?
3. Where is f concave up? Why?

### For Wednesday September 17

Section 1.7 The Geometry of Higher Order Derivatives

To read : All. Think about why the Second Derivative Test makes sense.

Reading Questions : Use the graphs of f, f ', and f ' ' in Figure 3 on page 67.
1. By looking at the graph of f '', how can you tell where f is concave up and concave down?
2. By looking at the graph of f ', how can you tell where f is concave up and concave down?

### For Friday September 19

Work on Project 1 today. No Reading Assignment.

### For Monday September 22

Section 1.7 The Geometry of Higher Order Derivatives

### For Wednesday September 24

Section 2.1 Defining the Derivative

To read : All. We'll talk about the formal defintion of the derivative in detail during class.

1. Let f(x)=x3. Find the slope of the secant line from x=-2 to x=4.
2. For a function f, what does the difference quotient ( f(a+h) - f(a) )/ h measure?
3. Let f(x)=x3. What is the average rate of change of f from x=-2 to x=4?

### For Friday September 26

Section 2.2 Derivatives of Power Functions and Polynomials

To read : Through Theorem 4 on page 97. Be sure to understand Examples 1 and 2.

1. What is the derivative of f(x)=x3?
2. Let f(x)=x1/3 (i.e. the cube root of x). Use the graph of y=f(x) to explain why f'(x) does not exist at x=0.

### For Monday September 29

Section 2.3 Limits

To read : Through Theorem 6. Be sure to understand Example 4 and the defintions of left-hand and right-hand limits.