MATH 2103. Exam 1A
Class #
NAME:
Problem 1A: The population of a bacteria in a lab experiment can be modeled by the function
P (t) = 300e0.09t where P is the number of bacteria after time t (in hours)
MATH 2103. Exam 3A
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NAME:
Problem 1:(14pts.) Consider the function f (x) = 2x3 3x2 36x + 1.
(a) (6pts.) Find ALL critical points of f (x).(show work)
f 0 (x) = 6x2 6x 36;
f 0 (x) = 0 x2 x 6 = 0
1. EQUAL DIGNITY RULE FOR ASSIGNMENT OF CONTRACTS SUBJECT TO THE
STATUTE OF FRAUDS
The equal dignity rule requires that if the contract being executed is or must be in
writing then the agents authori
Section 2.3 Interpretations of the Derivative
Example 1: The cost, C (in dollars) of building a house A square
feet in area is given by C(A) = 5000 + 75A.
The derivative C 0(A) can be written using L
Section 4.4 Profit, Cost and Revenue
Cost and revenue functions are shown below. Where does the maximum
profit occur?
Since profit is revenue minus cost, the profit is represented by the
between the c
Sections 1.41.5 Application to Economics and Exponential Functions
Example 1: A small e-Bay store makes and sells designer flip-flops. Their
monthly fixed costs are $234. Each item costs $12.50 to mak
Section 2.5-3.1 Marginal Cost and Revenue & Derivative Formulas for Powers
Example 1: The cost and revenue functions for a company are shown in the graph below.
(a) Is marginal cost greater at q = 20
Section 4.2 Inflection Points
Example 1: Determine where the function
f (x) = x3 6x2 + 9x + 4 is concave up and where it is concave down.
A point where the graph of a function f changes concavity is
c
MATH 2103. Quiz 2A
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NAME:
Problem 1: A car wash operator pays $3500 rent per month, then spends $10 per car wash,
which costs the consumer $15. Let x represents the number of cars they wash per
MATH 2103. Quiz 3A
Class #
NAME:
Problem 1: In 2010 the population of a city was 3000 people. Assuming that the population
is growing continuously at a rate of 4% per year
(a) (3pts) Find a formula fo
MATH 2103. Quiz 7A
Class #
NAME:
Problem 1: Calculate the following derivatives
df
= 3(4.1)x3.1 0 = 12.3x3.1
dx
1
d 1/2
5
5 dg
(b) (2pts.) g(t) = t + t ,
=
t + t = t1/2 + 5t4
dt
dt
2
1
(c) (2pts.) h(
MATH 2103. Quiz 1A
Problem 1:(4pts) Let W = f (t) represent wheat production in Argentina, in millions of
metric tons, where t is years since 2006. What is the meaning of f (5) = 18 in terms of wheat
Section 2.2 The Derivative Function
Definition: For a function f (x) we define the derivative function f 0, by
f 0(x) = Instantaneous rate of change of f at x.
Graph of the derivative using the graph
Section 4.3 Global Maxima and Minima
Find the local maxima and minima, and the global maximum and minimum
for the following graphs.
f (x) has a global minimum at x = p if f (p) is less than or equal
MATH 2103. Exam 3A
Class #
NAME:
Problem 1:(14pts.) Consider the function f (x) = x3 9x2 + 15x + 6.
(a) (6pts.) Find ALL critical points of f (x).(show work)
f 0 (x) = 3x2 18x + 15;
f 0 (x) = 0 3x2 18
MATH 2103. Exam 2A
Class #
NAME:
Problem 1: For some painkillers, the size of the dose, D, given depends on the weight of the patient,
W . Thus, D = f (W ), where D is in milligrams and W is in pounds
Section 1.1 What is a Function?
Definition: A function is a rule that takes certain numbers as
inputs and assigns to each a definite output. The set of all input
, and the set of all outputs is called
Sections 1.1-1.3 Functions, Linear Functions, Average Rate of Change
Example 1: A deposit is made into an interest bearing account. The balance
B(t) in dollars t years later is shown in the graph belo
Sections 1.7-2.1. Exponential Growth and Decay and Instantaneous Rate of Change
Example 1: The half-life of radioactive iodine is 3 days.
(a) Assuming a continuous model, what is the rate?
(b) What pe
Section 1.5 Exponential Functions
Example 1. The world population was approximately 6.1 billion
in the year 2000. Each year, the population grows by 1.2%. What
will be the population in 2020?
1
Sectio
Section 2.2 The Derivative Function
Example 1: The values of a and g(a) are shown in the table. Fill in the empty cells in the
g(b) g(a)
last row of the table by approximating the values of g 0 (a) us
Section 3.4 The Product and Quotient Rules
Example 1: Let f (x) = x and g(x) = x2. Find the derivatives of
f (x), g(x) and f (x)g(x).
The Product Rule:
If f (x) and g(x) are differentiable functions,
Section 1.4 Applications of Functions to Economics
Definition: The cost function, C(q), gives the total cost of
producing a quantity q of some good.
The variable cost for one additional unit is called
Section 3.3 The Chain Rule
The chain rule is used to find the derivatives of composite functions.
Examples of composite functions
y = ln(2x + 1)
The inside functions is
So, y = ln(2x + 1) can be writ
Section 3.1 Derivative Formulas for Powers and Polynomials
Previously, we were finding approximations of the derivative at a
given point by computing the average rate of change of a function on
a smal
Sections 1.51.6 Exponential Functions and Natural Logarithm
Example 1: Solve for t the following equations
(a) 14 = 5e0.3t
(b) 3e3t = 14e6t
Example 2: When John was 10 years old, his grandfather gave
Section 4.1 Local Minima and Maxima
Suppose p is an x-value in the domain of f .
f has a local minimum at p if f (p) is less than or equal
to the values of f for x-values near p.
f has a local maxim
MATH 2103. Quiz 11A
Class #
NAME:
t5 + e3t
Problem 1:(4pts.) Calculate derivative of f (t) = 3
t +6
(5t4 + 3e3t )(t3 + 6) (t5 + e3t )(3t2 )
df
=
dt
(t3 + 6)2
Problem 2:(6pts.) A total cost function, i
HW #2; Due on 10/19; MAX = 18
Class #
NAME:
Show work unless you are explicitly told not to.
DUE DATE: 10/19
Write your solutions on a separate sheets of paper,
stapled them and put your name and clas
HW #3; Due on 11/16; MAX = 38
Class #
NAME:
Show work unless you are explicitly told not to.
DUE DATE: 11/16
Write your solutions on a separate sheets of paper,
stapled them and put your name and clas