5. EXPONENTIAL FUNCTIONS
MATH 111
5
Exponential Functions
2
Upon this point, we have delt with functions which involve terms like x2 or x 3 , in other
words, terms of the form xp . For such a term, the base x is the input, whose value varies,
but the powe
STUDENTS
SOLUTIONS MANUAL
Introduction to Linear Programming
by L. N. Vaserstein
Last updated November 29, 2016
This manual includes:
corrections to the textbook,
additional references,
answers and solutions for exercises the textbook,
tips, hints, and re
Nonlinear Programming
3rd Edition
Theoretical Solutions Manual
Chapter 4
Dimitri P. Bertsekas
Massachusetts Institute of Technology
Athena Scientific, Belmont, Massachusetts
1
NOTE
This manual contains solutions of the theoretical problems, marked in the
Nonlinear Programming
3rd Edition
Theoretical Solutions Manual
Chapter 6
Dimitri P. Bertsekas
Massachusetts Institute of Technology
Athena Scientific, Belmont, Massachusetts
1
NOTE
This manual contains solutions of the theoretical problems, marked in the
Nonlinear Programming
3rd Edition
Theoretical Solutions Manual
Chapter 7
Dimitri P. Bertsekas
Massachusetts Institute of Technology
Athena Scientific, Belmont, Massachusetts
1
NOTE
This manual contains solutions of the theoretical problems, marked in the
MATH 408
FINAL EXAM
June 9, 2014
SOLUTIONS TO SAMPLE QUESTIONS
This exam will consist of three parts: (I) Linear Least Squares, (II) Quadratic Optimization, and (III) Optimality Conditions and Lagrangian Duality. The first two parts (I) Linear Least Squar
Nonlinear Programming
3rd Edition
Theoretical Solutions Manual
Chapter 3
Dimitri P. Bertsekas
Massachusetts Institute of Technology
Athena Scientific, Belmont, Massachusetts
1
NOTE
This manual contains solutions of the theoretical problems, marked in the
MATH 408
MIDTERM EXAM
May 9, 2014
OUTLINE
This exam will consist of two parts and each part will have 3 multipart questions. Each of the 6 questions
is worth 50 points for a total of 300 points. The two part of the exam are (I) Linear Least Squares and
(I
10-725/36-725 Optimization Midterm Exam
November 6, 2012
NAME:
ANDREW ID:
Instructions:
This exam is 1hr 20mins long.
Except for a single two-sided sheet of notes, no other material or discussion is
permitted.
There are 11 one-sided sheets. Please use the
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MATH 111
2
2. LINEAR FUNCTIONS AND AVERAGE RATE OF CHANGE
Linear Functions and Average Rate of Change
2.1
Average Rate of Change
Example 2.1
Suppose you take a trip and record the distance that you travel every few minutes. The distance s you have travele
f (x) = ax2 + bx + c
a b
a 6= 0
c
x
f (x) = 3x2 + x 7
Q(x) = (2x 3)2 + 4
a = 3, b = 1, c =
7
Q(x)
x
Q(x) = 4x
a=1
2
12x + 13
a = 4, b =
12, c = 13
f (x) = x2
b=c=0
f
f (x)
f (x) = ax2 + bx + c
x=
b
2a
(
x2
y = f (x) =
x+6
x y
1, c = 6
f a = 1.b =
1
1
=
2(