115 Exam 1: Formulas printed on the exam
Formulas printed on the exam
Function
f (x) = x n
Derivative
f '(x) = nx n1
f
g
f ' g fg '
g2
Formulas from algebra that you may need that are NOT printed on the exam:
y y1 = m(

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115 Lecture Notes Section 4.1
4.1 Derivatives of Powers, Sums and Constant Multiples
The definition of the derivative of f (x) says
f '(x) =
In Section 3.6 in examples in the text, we used the definition of the derivative to find formulas
for

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115 Lecture Notes Section 3.6
Section 3.6 Derivatives: Algebraic Viewpoint
When we say find the derivative f '(x) using the definition of the derivative we mean you
should calculate
Section 3.6 Practice
a. Compute the derivative f '(x) for f (

115 Off-line Homework Answers
1
Section 1.2
Cost
1a.
C(x) = 20 + 88x
1b.
$196
1c.
Variable costs: 88x dollars;
Fixed costs: $20
1d.
The scale for your axes may vary
from those shown here. For best
results, choose scales so that the
graph you are pres

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115 Lecture Notes Section 3.4
Section 3.4 Average Rates of Change
Slope of the line through (x1, y1) and (x2, y2)
Average Rate of Change of the function S(t)
between t1 and t2
S
=
t
m=
Section 3.4 Example 1
The following table and its correspo

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115 Lecture Notes Section 1.3
Section 1.3 Linear Functions and Models
Definition
A linear function is a function whose graph is a line. Linear functions have the form
f (x) =
where m is called the _, and b is called the _.
Point-slope formula

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115 Lecture Notes Section 1.2
Lecture Notes 1.2
An example of a model
In Example 1, Section 1.1, the author suggests that the total number of iPods sold by Apple up to
the end of year x can be approximated by f (x) = 4x 2 + 16x + 2 million iPo

Section 3.5 page 1
Math 115 Off-Line Homework
1. Consider the function R(t) = 270 + 20t3, which represents the value of an ounce of palladium
in U.S. dollars as a function of the time t in days.
a. Find the average rate of change of R over the intervals [

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115 Lecture Notes Section 3.5
Section 3.5 Derivatives: Numerical and Graphical
Derive the Difference Quotient Formula
The difference quotient for f (x) at x = a is the average rate of change of f on the interval
[a, a +h].
Example 4 Section 3.

Section 1.2 page 1
Math 115 Off-Line Homework
1. The cost of renting tuxes for the Choral Societys formal is $20 down, plus $88 per tux.
a. Express the cost C as a function of the number of tuxedos rented x.
Use your function to answer the following quest

Section 3.6 page 1
Math 115 Off-Line Homework
1. a. Compute the derivative of the function f (x) = 8x using the definition. Show your steps
df
=
and use correct notation, giving your answer as f '(x) = or as
dx
b. Find f '(4).
2. a. Compute the derivati

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115 Lecture Notes Section 4.3 Quotient Rule
Formula: Quotient Rule
If f and g are differentiable functions of x and g(x) 0, then the quotient f /g is differentiable, and
d f (x)
=
dx g(x)
Examples
a. Let f (x) = x2, and g(x) = 3x 1. Then
f
=

Section 1.3 page 1
Math 115 Off-Line Homework
1. If it costs Microsoft $1,230 to manufacture 8 Kinects per hour for the Xbox-360 and $2,430
to manufacture 16 per hour at a particular plant, obtain the corresponding linear cost
function.
a. Find the formul

Shiyao Li
Journal #4 Women in Modern America
Society Proceedings by Dr. Cushing
1. What womens cases are Cushing and the medical professionals discussing?
It is a case of Melancholia, masturbation, cured by removal of both ovaries.
Patient is a 33 years o