Lecture 1  Math Review.
Topics from Calculus you should know:
How to define a derivative
How to interpret
f
0
(
x
) =
2. What does that mean?
How to calculate the derivative of:
1
polynomials, ex.:
u
(
x
) =
3
x
4

5
x
2
+
6
2
exponential functions, ex.:
u
(
x
) =
e
x
2
+
2
3
logrithmic functions, ex.:
u
(
x
) =
x
ln
(
3
x
+
6
)
Know the product rule, quotient rule, and chain rule
Implicit differentiation
ECG 700
Lecture 1  Math Review
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Lecture 1  Math Review.
Topics from Calculus you should know (cont.):
The first derivative test.
The second derivative test.
Partial derivatives
Total differentiation
Topics you probably don’t know but will learn:
Legrange multipliers
Envelope Theorem
ECG 700
Lecture 1  Math Review
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Differentiation  a quick review
Definition
The derivative of a function at a:
d
dx
f
(
a
) =
f
0
(
a
) =
lim
x
→
a
f
(
x
)

f
(
a
)
x

a
or equivalently:
f
0
(
a
) =
lim
h
→
0
f
(
a
+
h
)

f
(
a
)
h
ECG 700
Lecture 1  Math Review
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Differentiation  a quick review
What does the derivative represent?
The slope of the tangent line at point a.
The “instantaneous” rate of change
For our purposes,
marginal = derivative
.
The marginal utility of good
x
is the change in utility resulting
from a change to the quantity of good
x
.
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 Fall '09
 Morrill
 Calculus, Derivative

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