A.1 Basic Operations
Pages 564 - 568
Definition
1.
Matrix a rectangular array of numbers, usually denoted by capital letters, whose dimension (size) is given by the
expression m n (where m is the number of rows and n is the number of columns).
2.
Entries
MATH WITH ACCOUNTS PRINCIPLE
Account analysis method.
1.
Variable costs:
Car wash labor
Soap, cloth, and supplies
Water
28,000
Electric power to move conveyor belt
Total variable costs
$240,000
32,000
72,000
$372,000
Fixed costs:
Depreciation $ 64,000
Sal
Variable costs in 2007:
Account
Unit
Variable
Cost per
Unit for
2006
(6)
Direct materials
Direct manufacturing labor
Power
Supervision labor
Materials-handling labor
Maintenance labor
Depreciation
Rent, property taxes, admin.
Total
$4.00
3.00
0.50
0.15
0.
Estimating a cost function, high-low method.
1.
See Solution Exhibit 10-23. There is a positive relationship between the number
of service reports (a cost driver) and the customer-service department costs. This
relationship is economically plausible.
2.
N
10-24 (3040 min.) Linear cost approximation.
1.
Slope coefficient (b)
=
=
Constant (a)
Cost function
= $43.00
= $529,000 ($43.00 7,000)
= $228,000
= $228,000 + $43.00 professional labor-hours
The linear cost function is plotted in Solution Exhibit 10-24.
SOLUTION EXHIBIT 10-24
Linear Cost Function Plot of Professional Labor-Hours
on Total Overhead Costs for Memphis Consulting Group
10-26 (25 min.) Regression analysis, service company.
1.
Solution Exhibit 10-26 plots the relationship between labor-hours an
Notes 4/27
Find the indefinite integral of
=x1/6.
Here is an example of an indefinite integral we cant do by hand:
Not all functions have simple indefinite integrals:
erf(x) is not a standard function and doesnt have a simple formula to plug values into.
A.2 Matrix Multiplication
Pages 569 - 578
1.1 Vector Multiplication
A natural question to ask is the multiplication of two matrices. One would think that like addition, we multiply corresponding
entries, but that is not the case.
First, lets consider the
2.3
Rates of Change: Velocity and Marginals
Pages 138 - 152
Average Rate of Change
The average rate of change of a function f ( x) over the interval [a, b] is given by the equation
f avg
f (b) f (a) y
ba
x
Example 1: Find the average rate of change of f
2.5
The Chain Rule
Pages 165 - 173
Recall the composition function y f ( g ( x). To decompose the function, choose f as the simple function (outer
function) and g as the messy or inner function. This process is not unique, but gives a decomposition of the
2.8
Related Rates
Pages 188 - 195
In this section, we will be studying problems involving variables that are changing with respect to time t.
Example 1: Suppose y 2 4 x 2 x 1 where if x 1, dx dt 2. Find dy dt when x 1.
Solution:
Since we need to find dy d
3.2
First Derivative Test
Pages 215 - 223
The relative extrema of a function f ( x) are where f ( x) is continuous, defined, and changes from increasing to decreasing,
or vice versa. The singular of extrema is extremum.
Definitions
Let f be a continuous f
3.4
Applications I Geometric Optimization
Pages 235 - 243
In this section, we discuss applications of the derivative to optimization. Sometimes, the function is multi -variable and may
require another equation, called a constraint equation, relating the v
4.3
Derivative of Exponential Functions
Pages 308 - 315
Theorem
dx
e ex
dx
and so if C constant number, then
d
dx
Ce x C
e Ce x
dx
dx
Notes:
dx
dn
e xe x 1 because it is only valid for variable base and constant exponent
x nx n 1
dx
dx
No other function
4.5
Logarithmic Functions and Derivatives
Pages 326 - 334
Logarithmic Function
Let a 0 such that a 1. The logarithmic function with base a, denoted by log a , is defined by
log a x y a y x
log a x is read as the log of x base a or the log base a of x
y l
5.5
The Area of a Region Bounded by Two Graphs
Pages 394 - 402
Area of a Region Bounded by Two Graphs
If f ( x) and g ( x) are continuous on [a, b] such that g ( x) f ( x) for all x in the interval, then the area of the
region bounded by the graphs of f (
1) a-e
Equation of line tangent:
Critical Points:
Critical Points
(-5.0283,
Decreasing at -5.0283, increasing at 0.1033, and decreasing at -16.04
Concave up from (-5.0283,-108.76) to (0.1033,-9.95), concave down from (0.1033,-9.95) to
, and concave up fro
Notes 4/27
Find the indefinite integral of
=x1/6.
Here is an example of an indefinite integral we cant do by hand:
Not all functions have simple indefinite integrals:
erf(x) is not a standard function and doesnt have a simple formula to plug values into.