Math for Econ I- Practice Problems
New York University
1. Supply and demand
1. In a California town, the monthly charge for waste collection is $8 for 32 gallons of waste and $12.32 for 68 gallons
of waste.
(a) Find a linear formula for the cost, C, of wa

Sum, product, and quotient rules
(6.7 MFE Book, 2.2, 2.3, 2.4 E-Book)
September 22, 2016
Sum, product, and quotient rules (6.7 MFE Book, 2.2, 2.3, 2.4 E
Sum and difference rule, Example 1
If f and g are differentiable at a, then
(f + g )0 (x) = f 0 (x) +

Functions of Several Variables (Ch. 11)
November 30, 2016
Functions of Several Variables (Ch. 11)
We used to deal with f (x), g (y ), (q), etc.
What if more than one independent variable?
Airline revenue is a function of full price tickets sold and
discou

Transforming graphs and functions; inverses: Ch 5
MFE book
September 13, 2016
Transforming graphs and functions; inverses: Ch 5 MFE book
Shifting graphs (5.1)
If we are given a function y = f (x), then to graph:
1
y = f (x) + c, shift the graph of f up c

Partial Derivatives (11.2, 11.3, 11.8)
November 30, 2016
Partial Derivatives (11.2, 11.3, 11.8)
In the past weve fixed one variable and varied the other a bit.
Now, we fix a variable and differentiate with respect to another:
Partial Derivatives (11.2, 11

Limits (6.5 MFE, 1.4 Stewart)
September 13, 2016
Limits (6.5 MFE, 1.4 Stewart)
In order to understand the concept of a derivative (sections 6.2
through 6.4), we must understand limits.
Limits (6.5 MFE, 1.4 Stewart)
What is a Limit?
So far, weve focused ev

Rates of Change and Derivatives
(6.1-6.4, 6.6 MFE Book, 2.1 E-Book)
September 22, 2016
Rates of Change and Derivatives (6.1-6.4, 6.6 MFE Book, 2.1 E-
Overview
Key concept: f 0 (a), called the derivative of f at a.
What it represents: The instantaneous rat

Optimization for functions of multiple variables
(Ch. 13 in MFE textbook; Section 11.7 in e-book)
December 1, 2016
Optimization for functions of multiple variables (Ch. 13 in MFE t
Let f be a function of multiple variables with domain D.
f has a local max

Math for Econ. I
Class Overview
Trush Majmudar
(Pronounced as troosh - may be one and a half Os)
September 6, 2016
Trush Majmudar (Pronounced as troosh - may be one and a half Os)
Math for Econ. I Class Overview
Office Hours
My office is 719 Warren Weaver

Math for Econ I- Practice Problems
New York University
Derivatives of exponentials and logs and inverse functions.
From the E-Book:
1. Section 3.2: 15, 17, 35, 39
2. Section 3.3: 5, 11, 29, 43, 53, 61, 63,
(The answers to all of these are at the back of t

Single Variable Optimization (Chapter 8)
November 1, 2016
Single Variable Optimization (Chapter 8)
Absolute maximum, minimum
Definition
Let f be a function with domain D.
f (c) is the absolute max value of f if f (c) f (x) for all x D.
We call c a maximum

Math for Econ I- Practice Problems
New York University
Derivatives of exponentials and logs and inverse functions.
From the E-Book:
1. Section 3.2: 15, 17, 35, 39
2. Section 3.3: 5, 11, 29, 43, 53, 61, 63,
(The answers to all of these are at the back of t

Original Draft: October 31, 1998
Reformatted and revised: May 30, 2001
The idea of social entrepreneurship has struck a responsive chord. It is a phrase well suited to our
times. It combines the passion of a social mission with an image of business-like d

Leadership
Social Entrepreneurship: The Case for
Definition
Social entrepreneurship is attracting growing amounts of talent, money, and attention. But along with its
increasing popularity has come less certainty about what exactly a social entrepreneur is

Implicit Differentiation (7.1)
October 18, 2016
Implicit Differentiation (7.1)
Motivation
Sometimes we arent given y as an explicit function of x.
x 2 + y 2 = 1,
y 3 + 4x 2 y = 10,
etc.
How do we find y 0 , if we cant even solve for y ?
Implicit Different

6. Linearization and Dierentials
1. Find the linearization L(x) of the function at a:
(a) f (x) = x4 + 3x2 , a =
p
(b) f (x) = x, a = 4
1
2. Find the local linearization of f (x) =
p
x at x = 4 and use this to approximate the value of
p
4.1.
3. Find the l

Calculus 1 (Math-UA-121)
Fall 2015
Homework 4
Section 2.1 and 2.2
Name:
HAVE FUN!
:)
1
Calculus 1 (Math-UA-121)
Fall 2015
Give complete, well-written solutions to the following exercises. Please upload one single
pdf.
1. The graph shows the position funct

Calculus 1 (Math-UA-121)
Fall 2015
Homework 6
Section 2.5, 2.6 and 2.8
Name:
HAVE FUN!
:)
1
Calculus 1 (Math-UA-121)
Fall 2015
Give complete, well-written solutions to the following exercises. Please upload only one
pdf.
1. Using the information in the gi

Math for Econ I-Homework Assignment 10
Due Monday 6th of May beginning of class
Selin Kalaycioglu
New York University
Read Sections 11.1, 11.2, 11.3, 11.7, 11.8
Please make sure you write out the solutions neatly. Please show all your work. If you only wr

Math for Econ I-Homework Assignment 4 (15 pts)
Due Monday 25th of February, beginning of class
Selin Kalaycioglu
New York University
Please make sure you write out the solutions neatly. Please show all your work. If you only write the answer with no
work

Math for Econ I-Homework Assignment 6
Due Monday 1st of April, beginning of class
Selin Kalaycioglu
New York University
Read sections 6.9, 6.10, 6.11, 7.1, 7.2
Please make sure you write out the solutions neatly. Please show all your work. If you only wri

Math for Econ I-Homework Assignment 7
Due Monday 8st of April, beginning of class
Selin Kalaycioglu
New York University
Read sections 7.4 and 7.7
Please make sure you write out the solutions neatly. Please show all your work. If you only write the answer

Math for Econ I-Homework Assignment 1(33 pts)
Due Monday , beginning of class
Selin Kalaycioglu
New York University
From our textbook read Chapter 4!
Please make sure you write out the solutions neatly. Please show all your work. If you only write the ans

Math for Econ I-Homework Assignment 2
Due Monday February 11, beginning of class
Selin Kalaycioglu
New York University
From our textbook read Chapter 5!
Please make sure you write out the solutions neatly. Please show all your work. If you only write the

Math for Econ I-HW 5
Due Monday March 4th, beginning of class
Selin Kalaycioglu
New York University
From our book please read sections 6.1-6.4, 6.6.
1. Use the figure below to fill in the blanks in the following statements about the function g at point B.

Math for Econ I-Homework Assignment 9
Due Monday April 29th beginning of class
Selin Kalaycioglu
Job: 9-miscaq14-main Sheet: 1 Page: 1 (April
2012University
08 : 44) [9-miscaq14-main]
New5,York
Please make sure you write out the solutions neatly. Please s

Math for Econ I-Homework Assignment 3
Due Wednesday 20th of February, beginning of class
Selin Kalaycioglu
New York University
In this HW, I included problems again that covers more of the review material to make sure that everybody is solid
on those. It

5. Product, Quotient, and Chain Rules
1. Compute derivatives for the following functions. You do not need to fully simplify your answers to (c) and (d).
p
(a) x 1 (x2 + 1) x
x+1
(b)
x 1
p
x 2
(c) p
x+1
(x + 1)(x 1)
(d)
(x2 + 2)(x + 3)
Solution:
3 1/2 1 3/

Math for Econ I- Practice Problems
New York University
1. Supply and demand
1. In a California town, the monthly charge for waste collection is $8 for 32 gallons of waste and $12.32 for 68 gallons
of waste.
(a) Find a linear formula for the cost, C, of wa

5. Product, Quotient, and Chain Rules
1. Compute derivatives for the following functions. You do not need to fully simplify your answers to (c) and (d).
p
(a) x 1 (x2 + 1) x
x+1
(b)
x 1
p
x 2
(c) p
x+1
(x + 1)(x 1)
(d)
(x2 + 2)(x + 3)
2. Compute derivativ