Name: 1. Find the domains of the following functions: (a) f (x) = log(x(x + 1)
1
Logs only take positive values, so th domain will be x values such that x(x + 1) > 0. The critical points for this in
Find the four second order partial derivatives
1.
f ( x , y ) =8 x3 +5 y 38 x 2 y 2 +100
2.
f ( x , y )=
6 x 26 y 2
x2 + y2
Find all relative extreme points
1.
3 2
2
f ( x , y ) =x y +6 x +21 y+ 8
2
2
Final Exam Review Fall 2016
1.
a.
x 5 f ( x )
lim
b.
x 5+ f ( x )
lim
c.
x 5
d.
x 1
e.
lim f ( x )
DNE
lim f ( x )
lim f ( x )
x 1
4
1
f. Is f(x) continuous at x = 1? What are rules for something to
6.2
Suppose the demand for a product is given by p=d(q)=0.8q+150p=d(q)=0.8q+150 and the
supply for the same product is given by p=s(q)=5.2qp=s(q)=5.2q. For both functions, qq is the
quantity and pp is
Partial Derivatives
Find
z z z
,
,
x y x

(3,2)
1.
z=8 x4 xy
2.
z=10 x7 y
3.
z=2 x3 +3 xyx
4.
f ( x , y ) = x 2 + y 2
z
y

( 0,4 )
Higher Order Partials
Find the four second order partial derivativ
Mixed Review Chapter 4
Take the following derivatives:
1.
f ( x )=ln ( x 2x )
2.
f ( x )=6 x
3.
f ( x )= 2 x ln ( 4 x )
4.
f ( x )= x + ln x
2
2
Antiderivatives
Take the antiderivative of the followi
Warmup: First Derivative Test Quiz
Refer to the figure for Questions 14.
2
1
1
3
1
1.
On what interval is f(x) positive?
a. (0, )
2.
1
b. [1,)
c. [2,)
d. (2,)
e. (,2)
b. 0 and 2
c. 0
d. 0 and 3
e.
SI Session: Optimization
Optimization Pro Tips!
Word problems are some of the most difficult concepts for students to master, because they
come in so many shapes and forms and dont always have a clear
Chapter 2 Review: Implicit Differentiation Worksheet
dy
x ) for each function.
Find y (aka
2
2
1.
5 y 11 x =9
2.
( 2 y 3+ 5 x 2 ) =6 x 2 +11
3.
6 x4 x5 y 3 + y 5=1
4.
6 x + 4 x y =7 x1
3
2
Find y (aka
Warmup Review of 1.6
Find the Average Rate of Change of f ( x ) with respect to
1)
f ( x )=2 x1; [ 4,9 ]
2)
x 25
f ( x )=
; [ 6,15 ]
x5
2
Find and simplify the difference quotient of:
3)
f ( x )=6 x1
Basic Integration Techniques
Find the antiderivative. Dont forget to add C!
(
4 7
+ x
x3 x
)
1.
2.
6 x
3.
( 3 x 24 x+7 ) x
4.
3 3
2 6 x + x 4 x
x
5.
x 4 x x
6.
( 2 t 5 3 ) t 4 t
8x
(
)
5
Solving
WarmUp
True/False
1)
2)
3)
4)
5)
6)
The first derivative of an equation is used to determine critical values
Setting f(x) = 0 allows you to determine hypercritical values
If f(x) is defined at x=c, t
4.1 Applications
Find f(x) that satisfies the conditions given. [HINT: Take the indefinite
integral and solve for C]
1.
f ' ( x )=5 x2 +3 x7 ;
2.
f ' ( x )=5 2 x ;
f ( 0 )=
3.
f ' ( x )=x 2+1 ;
f ( 0
Name_
Mixed Review Chapter 4
Take the following derivatives:
1.
f ( x )=ln ( x 2x )
2.
f ( x )=6 x
3.
f ( x )= 2 x ln ( 4 x )
4.
f ( x )= x + ln x
2
2
Name_
Antiderivatives
Take the antiderivative of
1 Practice Test 2 1. Take the derivatives of the following functions: (a) f (x) = 4 3x3 + 2x + x (b) g(x) =
1 (x3 +2x2 +3x1)4
2. Find the equation of the tangent line to F (x) =
2x2  4x + 1 at
Essay I Assignment: Summary and Response
Your assignment is to write a summary of and response to one of the essays from the Unit I reading assignments.
Steps in the process: Choose one of the essay
DICTIONARY FOR WOMEN'S PERSONAL ADS
40ish Adventurous Athletic Average looking Beautiful Contagious Smile Emotionally secure Feminist Free spirit Friendship first Fun New Age Openminded Outgoing Pas
Harper 1
Bianca Harper Eng 1304.42 Ms Schrock 25 February 2008
Review Questions 1) The five types of claims are claims of fact, claims of definition, claims of cause, claims of value, and claims of
Name_
Warmup: Optimization Practice
Solve the following optimization problems:
1. A wholesale store can sell 40 ceramic filters each week when it prices them at $100
each. The manager estimates that f
SI Session Chapter 3.4 and Chapter 3 Review
Warmup
Price Elasticity of Demand
Use your notes to answer the following conceptual questions about price elasticity of
demand.
1. What is the formula for
Chapter 1 & 2 Review
Warm up
True/false:
1) If
2) If
lim f ( x )
x 5
lim f ( x )
x 2
exists, then f(5) must exist.
= L, then L = f(2)
3) If f is continuous at x = 3, then
lim f ( x ) =f ( 3 )
x 3
.
4)
First and Second Derivative Test
Determine the relative min/max, intervals of increase/decrease, concavity and hypercritical
values of each function.
1.
f ( x )=2 x 3+ 2 x 210 x5
2.
4 3
2
f ( x )= x 9
Final Exam Review Fall 2016
1.
a.
x 5 f ( x )
lim
b.
x 5+ f ( x )
lim
c.
x 5
d.
x 1
e.
lim f ( x )
lim f ( x )
lim f ( x )
x 1
f. Is f(x) continuous at x = 1? What are rules for something to be cont
6.1 Area Between Curves
Area Between Two Curves
Find the area between two curves using integration:
1) The area bounded by the functions f ( x )=x +5 , g ( x ) =x2 +2 x+ 2 , and the lines x
= 0 and x
Warmup Activity
True or false.
1) A limit may exist as x approaches a even though the value f(a) may not exist.
2) A limit as x approaches a cannot be different from the function value f(a).
3) If the