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
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,
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)
.
Precalculus H
Name:_
Ch.1 Review
Period:_Date:
DO NOW:
1. Use the graphs of y k ( x) and y j ( x) to evaluate:
a) ( j 1 k )(2)
b) (k 1 j 1 )(10)
2. Solve for x:
x
1 2x 5
2
x 1 x x x
2
3x 4
3. Find the inverse function for f x x 4 . Find its domain and ra
2.2-2.5(day1)
DO NOW:
Write the General Form and Standard Form of the Quadratic Function that has the
indicated vertex and whose graph passes through the given point.
1. Vertex: (4, -1) Point: (0, 9)
2. Vertex: (-1/4, 3)
STANDARD:
STANDARD:
GENERAL:
GENER
1.5
DO NOW:
1. Use the fact that the graph of y f ( x) is increasing on the interval (0, 7) and
decreasing on the intervals (, 0) (7, ) to find the intervals on which the graph is
increasing and decreasing.
a) y f ( x)
b) y f ( x 2) 1
c) y 2 f ( x )
2. De
1.4
DO NOW:
5 x
f
(
x
)
1. Find the domain of
x 2 1 . Give your answer in interval notation,
and graph on the number line.
2. Find the difference quotient
f x h f ( x)
h
5
f
(
x
)
if
3x 2
Shifting Graphs
Let c be a positive real number.
1.
Vertical shift
Slop of a Line
1.
2.
3.
4.
1.1 1.2
y y
m 2 1
x2 x1
increasing if m 0
decreasing if m 0
horizontal if m 0
vertical if undefined slope
Slop-Intercept form of the Equation a Line:
Point-Slop form of the Equation a Line:
y mx b
y y1 m( x x1 )
Linear Function
2.2-2.5(day1)
DO NOW:
Write the General Form and Standard Form of the Quadratic Function that has the
indicated vertex and whose graph passes through the given point.
1. Vertex: (4, -1) Point: (0, 9)
2. Vertex: (-1/4, 3)
STANDARD:
STANDARD:
GENERAL:
GENER
Precalculus H
1.5 Combinations of functions
Name:_
Date:_ Period:_
Use the graphs of f ( x) and g ( x) shown below to find the indicated function value (if
possible).
1)
f g (2)
2)
f
g (3)
3) g ( f (3)
4)
f g (1)
Find f ( g ( x) and g ( f ( x) and stat
2.2-2.5(day3)
DO NOW:
1. Find all zeros of f ( x ) x 2 x 4 x 10 x x 8 x 4 and write the
polynomial as a product of linear factors. Then sketch the graph of f ( x ) .
6
5
4
3
2
2. Write any equation of a polynomial that satisfies the following conditions.
2.6 2.7 (Day 1)
DO NOW:
Find all asymptotes of each rational function.
2x
f
(
x
)
a)
x2 1
x2 x 2
b) f ( x ) 2
x x6
x4 2x2 8
c) f ( x ) 3
x x2 4x 4
3 x
f
(
x
)
d)
x 4
Definition of Vertical and Horizontal Asymptotes
1. The line x a is a vertical asymptote
DO NOW:
1.
Find the difference quotient if
a) f ( x)
2
x 5
b) f ( x) 6 x
1.3
Example #1:
Find the domain of each function. Give your answer in interval notation.
a)
f ( x)
1
2x 1
c)
f ( x)
1
1 x2
b)
h( x ) 4 x 2
d)
g ( x)
x2
x 3
Vertical Line Test: I
2.2-2.5(day2)
DO NOW:
1. Identify:
a) each zero of the given polynomial
function and state its multiplicity.
b) minimum degree of the given
polynomial function.
c) Write the equation of the given
function.
3
2
2. Name all possible rational zeros of f ( x
2.2-2.5(day2)
DO NOW:
1. Identify:
a) each zero of the given polynomial
function and state its multiplicity.
b) minimum degree of the given
polynomial function.
c) Write the equation of the given
function.
3
2
2. Name all possible rational zeros of f ( x