Mrs. Cisnero
AP CALCULUS BC, Chapter 1 Review day 1
Pg. 92: 48, 49, 51, 52, and 70.
48.
Determine the values of b and c such that the function is continuous on the
entire real line.
x 1
f ( x) 2
x bx c
49.
51.
3
on the interval 1,2 .
x2 4
Let f ( x)
.

AP CALCULUS BC
Section 2.1 (day 1) Introduction to Velocity C/W-H/W
Zack and Evan decide to get together one Friday night to study the beauty of
Calculus at a restaurant 7.5 km from their houses. Unfortunately, Zack is 10
hours late to their get together

AP CALCULUS BC
Section 2.1: The Derivative and the Tangent Line Problem, pg. 96
DO NOW: Lets revisit the concept of the derivatine of a function at a point, from last
school year, thru the following presentation.
Sketchpad Demo calc in Motion: Derivative

AP CALCULUS BC
Section 2.1: The Derivative and the Tangent Line Problem, pg. 96
DO NOW: Lets revisit the concept of the derivatine of a function at a point, from last
school year, thru the following presentation.
Sketchpad Demo calc in Motion: Derivative

AME:
2.1 -Day 3
9/22/08
Describe the values in the domain of each function at which f is continuous and the
values at which f is differentiable. Next, conceptually sketch a graph of what the
derivative of the function would look like.
f ( x) = x 2
f ( x)

2.1 - Differentiability and Continuity
(Day 3)
Consider the function f ( x) = cos( x)
a. Sketch the function on the interval [ 2 , 2 ] and label any roots (NO TI-JOE)
b. I claim that f (x) is continuous on this interval, but is not differentiable at four

AP CALCULUS BC
2.1 - Differentiability and Continuity
EXTRA REVIEW QUESTIONS
Consider the function f ( x) cos( x)
a. Sketch the function on the interval 2 , 2 and label any roots (NO TI-JOE)
b. I claim that f (x) is continuous on this interval, but is not

AP CALCULUS BC
Section 2.1 (day 2) CLASSWORK - 2
Describe the values in the domain of each function at which f is continuous and the values at
which f is differentiable. Next, conceptually sketch a graph of what the derivative of the function
would look l

AP CALCULUS BC
Section 2.1 (day 2) CLASSWORK
The following is the graph of the derivative of a function:
In interval notation, determine where the original function:
a)
b)
c)
d)
Is increasing
Is decreasing
Has extrema (x-coordinates)
Conceptually sketch a

AP CALCULUS BC
Section 2.1 (day 1) Introduction to Velocity C/W-H/W
Zack and Evan decide to get together one Friday night to study the beauty of
Calculus at a restaurant 7.5 km from their houses. Unfortunately, Zack is 10
hours late to their get together

AP CALCULUS BC
Section 2.1 HOMEWORK
SHOW ALL WORK IN YOUR NOTEBOOK
1.
State the limit definition of a derivative?
Given the following functions:
a.
Find the derivative f ' ( x) using the limit process
b.
Find the slope of the tangent line at the indicated

AP CALCULUS BC
Section 2.1 (day 2)
Heres an old friendly function
f ( x) x 2
Please provide a quick sketch below and whats the domain of this function?
Using the below definition of a derivative, find f (x ) - Remember the chapter on limits!
f ( x) lim
h

AP CALCULUS BC
Section 2.1 (day 2)
Heres an old friendly function
f ( x) = x 2
Please provide a quick sketch below and whats the domain of this function?
Using the below definition of a derivative, find
f ( x) = lim
h 0
f ( x + h) f ( x )
h
Whats the doma

AP CALCULUS BC
Section 2.1 (day 2) CLASSWORK
The following is the graph of the derivative of a function:
In interval notation, determine where the original function:
a) Is increasing
b) Is decreasing
c) Has extrema (x-coordinates)
d) Conceptually sketch a

Mrs. Cisnero, AP CALCULUS BC
CHAPTER 1 NOTES
Introduction to Limits
Sometimes you cant work something out directly but you can see what it should be
as you get closer and closer!
Lets use this function as an example:
x2 1
f ( x)
x 1
And lets work it out

Mrs. Cisnero, AP CALCULUS BC
CHAPTER 1 NOTES
Introduction to Limits
Sometimes you cant work something out directly but you can see what it should be
as you get closer and closer!
Lets use this function as an example:
x2 1
f ( x)
x 1
And lets work it out

Mrs. Cisnero
AP CALCULUS BC, Chapter 1 Review day 1
Pg. 92: 48, 49, 51, 52, and 70.
48.
Determine the values of b and c such that the function is continuous on the
entire real line.
x +1
f ( x) = 2
x + bx + c
1< x < 3
x 2 1
Mrs. Cisnero
AP CALCULUS BC,

AP CALCULUS BC
Section 2.1 HOMEWORK
SHOW ALL WORK IN YOUR NOTEBOOK
1.
State the limit definition of a derivative?
AP CALCULUS BC
Section 2.1 HOMEWORK
Given the following functions:
a.
Find the derivative f ' ( x) using the limit process
b.
Find the slope