ECON 3030 Columbia University in the City of New York Economics Worksheet
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Econ 3030 Assignment 1
Due February 9, 2022
Instructions: All assignments must be submitted into its corresponding Assignment folder on UM Learn.
All files must be in pdf or MS-Word. Submit one file per assignment.
1. Find the critical value and determine whether it is a maximum, minimum or inflection point.
Show each step:
a) ???? = (8 ? ????)2
b) ???? = 25 + (???? + 2)2
c) ???? = 14 + (7 ? ????)3
2. Use the principle from the Nth derivative test to find the critical value and determine whether it
is a maximum, minimum or inflection point. (You do NOT need to take 24 derivatives. You also
do not need to give me details about inflection points. )
d) ???? = 12 + (4 ? ????)24
e) ???? = 10 + (3???? + 6)31
f) ???? = 6 + (4 ? ????)25
g) ???? = 15 + (3???? + 6)32
3. Write the 2nd order Taylor Series for the following function, expanded around ????0 = 4, with
remainder. Use ???? in the remainder term for this question. (recall, 2nd order means that the
highest derivative is the 2nd, before the remainder term).
???? = 20 + (???? ? 3)3/2
4. In one diagram, draw the graphs for
a. ???? = 3???? and
b. ???? = 0.5 (3???? )
Do these have the same vertical intercept?
Do they have the same horizontal intercept?
5. Noting that the derivative of ???? ???? is ???? ???? , use the chain rule to find the derivative of
a. ???? = ???? 3????
b. ???? = ???? ?3????
c. ???? = 2???? 3????
d. ???? = ???? 3????+1
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Explanation & Answer:
5 Questions
Tags:
economics
principle
derivative test
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