Chapter 6
APPLICATIONS OF THE DERIVATIVE
6.1 Absolute Extrema
. As shown onthe graph, the absolute maximum oc-
curs at $3; there is no absolute minimum. (There
is no functional value that is less than all others.)
. As shown on the graph, the absolute m
APPLICATIONS OF THE DERIVATIVE
11- [(93) = r173 651:2 + 934' " 83 IO 5]
/
6.1 Absolute Extrema
10.
376
As shown on the graph, the absolute maximum oc
curs at .703; there is no absolute minimum. (There
is no functional value that is less than all others.)
452
7 2. (a) First nd 71(t) by integrating a(1;):
When t
and 'u(t)
mt) = /(32)dt = 32t + k.
= 0, 22(1) = 710:
v0 = 32(0) + k
Uo = k
= 32'L' + 00.
Now integrate v(t) to nd 5(11).
5(4) = /(32t+vo)d1;
= 16t2 + vot + 0
Since 3(t) = 0 when t = 0, we can subs
GRAPHS AND THE DERIVATIVE
(b) Since the graph of the function is negative for
-1 < a: < 3, the interval where f (1:) is decreasing
is (1,3).
_
5.1 Increasing and Decreasing
Functions
10. (a) Since the graph of the function is positive for
3 < a: < 5, the
14"(t) = (115.9)(6 "I W)
1 4/1 3 (d) torque decreases with engine speed on
+ (175390 (17? ) (3000,3500) and (6000,7200).
= (175.9)(_t/1'3) (1 cfw_3) ' 60. (a) As :1: increases, j(93) decreases, so f is
' decreasing for these Litvalues. Therefore,
w 175.96
Consumption and Saving
Consumption and Current Income (Keynes)
Intertemporal Budget Constraint (Fisher)
The Life-Cycle Theory (Modigliani)
The Permanent-Income Theory (Friedman)
The Random-Walk Model (Hall)
Liquidity Constraint and Myopia
The Barro-Ricard
Chapter 7
INTEGRATION
7.1 Antiderivatives
1. If F(:r) and G(x) are both antiderivatives of f(a:),
then there is a constant C' such that
F(C) C(x) = C'.
The two functions can dier only by a constant.
5./6dk=6/1dlc
:/lk0dy
#0 + O
=6k+0
6./9dy=:/1dy=9/y0dy
0
1. x2 independence test
Ho: medication and being cured are independent
Ha: medication and being cured are not independent
x2 = 54.0179
p = 0 0 < .05 reject the null hypothesis
df = 1
We have sufficient evidence to conclude that receiving the medication an
1 The pvalue
can be arty value
can be any positive value
can be any value, negative or positive
3- must be a numb-er between zero and 1
2 In hypothesis testing, the tentative assumption about the population paameter is
the alternative hypothesis
1- the nu
1. The P-value
Must be a number tween zero and 1
2. In hypothesis testing, the tentative assumption about the
population parameter is
The null hypothesis
3. The p-value
Is a probability
4. In interval estimation, as the sample size becomes larger, the
int
When individuals in a sample of 150 were asked whether or not they supported capital
punishment, the following information was obtained.
Do you support
Number of
capital punishment?
individuals
Yes
40
No
60
No Opinion
50
Ho: Py = Pn = Pno = 1/3
Ha: At lea
Stats Exam 1 Notes
Numbers to know infinite degree of freedom look up t table!
Sampling problems: Normalcdf(lower,upper, mean,SD/SRn)
EX. Mean=60 DS=3
greater than 61.
Sample=100 find the probability that the sample mean is
CALCULATOR normalcdf(61,9999,60
QUANT 2600 Business Statistics I
Chapter 3: Descriptive Statistics: Numerical
Measures
Mathematical Concepts
Set of Data and Notation
= 1,2, ,
Defines a set of n observations on the X variable.
Or equivalently 1 , 2 , 3 , 4 , , ,
Example:
= 11, 3, 8, 2
QUANT 2600 Business Statistics I
Chapter 4: Introduction to Probability
Probability
How do you deal with making a decision when facing
uncertain outcomes?
What are the chances that sales will decrease if we increase prices?
What is the likelihood a ne
QUANT 2600 Business Statistics I
Chapter 2: Descriptive Statistics: Tabular and
Graphical Displays
Tabular and Graphical Displays Overview
Data
Categorical Data
Tabular
Displays
Frequency
Distribution
Rel. Freq. Dist.
Percent Freq.
Distribution
Graphic
QUANT 2600 Business Statistics I
Chapter 1: Data and Statistics
What is Data?
Data has shape!
So what does it look like?
Examples: Collect data
How many times do you eat pizza per week?
What can we say from the shape of the data?
What does the middle nu
QUANT 2600
PROFESSOR MATT GNAGEY
MIDTERM EXAM #1
CAR WASH
NAME:
PART I (40pts)
State
Arizona
Arkansas
California
Colorado
Idaho
Iowa
Kansas
Louisiana
Minnesota
Missouri
Montana
# of Car
Washes
287
122
1,730
283
90
213
158
143
189
342
79
# of
Workers
3,817
Practice Problems Worksheet
SECTION DUE DATE
Chapter 1
7/2/2016
Practice
1.2
Practice
1.4
Practice
1.5
Chapter 2
7/2/2016
Practice
2.1
For questions 1 and 2, you may skip a., and b.
Practice
2.2
https:/www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-
QUANT 2600
4.5 Extra Probability Problems
1. Fred has a total 450 friends on Facebook. 150 of his friends are female. 200 of his friends are married.
80 of his friends are female and married.
Define Event A: married
Define Event B: female
Describe in word
QUANT 2600
3.1 In-Class Exercise
Formulas:
Index Calculation for Percentiles:
( 100P )n
i=
Weighted Mean
if i is not an integer round up, if i is an integer average i and
i+1
Observation #
1
2
3
4
5
6
7
8
9
10
Below is fast food data from three popular ch
QUANT 2600
4.5 Extra Probability Problems
1. Fred has a total 450 friends on Facebook. 150 of his friends are female. 200 of his friends are married.
80 of his friends are female and married.
Define Event A: married
Define Event B: female
Describe in word
QUANT 2600
1.1 In-Class Exercise
1. Classify the following data that would be collected from the following questions as categorical or
quantitative. Then classify is as nominal, ordinal, interval, or ratio.
a. Do you commute to campus: Walk (1), Bus (2),
Practice Problems Worksheet
SECTION
Chapter 1
Practice
Practice
Practice
Chapter 2
Practice
Practice
Practice
Practice
Chapter 3
Practice
Practice
Practice
Chapter 4
Practice
Practice
Practice
Practice
Practice
DUE DATE
7/2/2016
1.2
1.4
1.5
7/2/2016
2.1
2