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CHAPTER 4 APPLICATIONS OF DIFFERENTIATION
4.7
OPTIMIZATION PROBLEMS
The methods we have learned in this chapter for nding extreme values have practical
applications in many areas of life. A businessperson wants to minimize costs and maximize prots.
Math 100 Assignment #5 Fall 2014
Before the quiz on October 15
Paper Assignments are NOT to be handed in. Use the assignment to prepare for the inclass quiz. These assignments are chosen to be an absolute minimum amount of work. For
most students they wil
Math 100 Assignment #7 Fall 2014
Before the quiz on October 29
Paper Assignments are NOT to be handed in. Use the assignment to prepare for the inclass quiz. These assignments are chosen to be an absolute minimum amount of work. For
most students they wil
Math 100 Assignment #6 Fall 2014
Before the quiz on October 22
Paper Assignments are NOT to be handed in. Use the assignment to prepare for the inclass quiz. These assignments are chosen to be an absolute minimum amount of work. For
most students they wil
SIMON FRASER UNIVERSITY
DEPARTMENT OF MATHEMATICS
Midterm 1 v2
MATH 100 D100 Fall 2015
October 05, 2015. 8:30 9:20 am
Name: (please print)
family name given name
SFU ID: @sfuca
_._._
student number SFUemail
Signature:
Instructions:
1. Do not open this b
Quadratic Functions
Objectives
Quadratic functions
Parabolas
Vertex
Completing the square
Vertex at minimum or maximum value
Quadratic formula
Distance between two points
Equation of a circle
Quadratic functions and parabolas
A quadratic function is a fun
Polynomials
Objectives
Polynomials
Degree of polynomials
Zeros of a function
Zeros and factors of a polynomial
Number of zeros of a polynomial
Multiplicity of zeros
End behaviour of polynomials
Polynomials
A polynomial is a function of the form
p(x) = an
Math 100 Assignment #4 Fall 2014
Before the quiz on October 8
Paper Assignments are NOT to be handed in. Use the assignment to prepare for the inclass quiz. These assignments are chosen to be an absolute minimum amount of work. For
most students they will
c n 21:; A = cfw_w A = gee V = Ewe V = eae :3 = a + 1:? Special Right Triangles
The number of niegreee ef are in a circle is 36th.
The measure ofdegrees of a straight angle is 180.
The sum of the measures in degrees of the engiee of a triangle is 180.
Homework 4
This homework has three sections: (a) textbook questions; (b) instructor questions. You need to
practice (a) and (b) .
a) Textbook questions:
Section 1.5: 3,7,9, 17, 21, 23, 29, 35,39
Section 1.6: 19, 21, 23, 37
Section 1.4: 31, 37, 39, 43, 45,
ASSIGNMENTS
Assignment 5
Precalculus
Math 100  D100 (Spring 2016)
All the assignments are posted together:
Quiz date: Wednesday, February 24, 2016
Complete this assignment by Tuesday in your homework journal. This will give you enough of time
to make su
Math 100
SAMPLE
Midterm 2
1. Determine whether the statement is True or False.
2
True False Solutions of
the quadratic equation ax + bx + c = 0 are given by
2
b b 4ac
x=
and they are always real numbers.
2a
True False The
p distance between points (x1 ,
Math 100
Solutions
Final Exam
1. [6] In mathematics and computer science, the ceiling function f (x) =
dxe is defined in the following way:
for every real number x, f (x) = dxe is the smallest integer that is
greater than or equal to x
(a) Complete the fo
Homework 4: key
(a) see the book
(b)
1. Sketch the graph of f and determine whether it is onetoone. Explain.
x4
f ( x)
2
( x 4)
if x 0
if x 0
The function is not onetoone because for y=1 there are more than one input (x=3
and x=5). We can also see t
AREA of a:
square
rectangle
parallelogram
triangle
trapezoid
circle
PERIMETER of a:
square
rectangle
triangle
CIRCUMFERENCE of a circle
VOLUME of a:
cube
rectangular container
square pyramid
cylinder
cone
COORDINATE GEOMETRY
PYTHAGOREAN RELATIONSHIP
MEASU
P . t Square
enme er Rectangle
Circumference Circle
Square
Rectangle
NEH Triangle
TraF'eIcIid A = cfw_h1+h2hf2
Circle A = pi*r1
Cube
Cylinder
Surface Area Cene
Sphere
Cylinder
Velume Cane
Sphere
Midpcaint Ferrnula M = llX1+X2llev1+y2lf2l
Integer Exponents
Objectives
Power functions
Algebraic properties of exponents
Root as inverse function
Rational exponents
Power functions
Power functions are functions of the form f (x) = x n where n is a
positive integer. Graphs of f (x) = x n where n =
Linear Functions and Lines
Objectives
Slope of a line
Equation of a line
Parallel and perpendicular lines
Linear functions
Slope of a line
If (x1 , y1 ) and (x2 , y2 ) are any two points on a line, with x1 6= x2 ,
then the slope of the line is
y2 y1
x2 x1
3.2 and 3.3 Rules for Logarithms
1. Quote. Lets not go and ruin it by thinking too much.
Clinton Eastwood, Jr., American actor, film director, producer, and composer, 1930
2. Problem: A day after your graduation you realize that the total amount of your s
2.5 Rational Functions
1. Quote. It has been said that man is a rational animal. All my life I have been searching for
evidence which could support this.
Bertrand Arthur William Russell, 3rd Earl Russell, British philosopher, logician, mathematician, hist
2.2 Quadratic Functions and Conics
1. Quote. Art is not a mirror to reflect the world, but a hammer with which to shape it.
Vladimir Vladimirovich Mayakovsky, Russian poet, playwright, artist and stage and film
actor, 1893 1930
2. Problem: A hockey team p
2.5 Rational Functions
9. A Taste Of Calculus. Sketch the graphs of the following rational functions:
1. f (x) =
x4 + 2x
x2 1
(a) Domain: Let p(x) = x4 + 2x and q(x) = x2 1. Then f (x) =
x4 + 2x
p(x)
=
.
2
x 1
q(x)
Solution : We note that that
q(x) = x2 1
3.1 Logarithms as Inverses of Exponential Functions
1. Quote. Startups are the engines of exponential growth, manifesting the power of innovation.
Narendra Damodardas Modi, Prime Minister of India, 1950
2. Problem: Solve
10x = 3.
3. Reminder: For all a, b