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 ne
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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
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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
Sectio
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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=
Sec
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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 ca
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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 ca
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. Fi
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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 chan
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 re
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)
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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)
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
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, cu