In economics, the concept of elasticity describes the sensitivity of quantity sold, Q, to the
price, P, at which an item is offered. There are two common ways that youll see
elasticity defined.
(A)
If
QUADRATIC EQUATIONS
A quadratic equation is always written in the form of:
ax2 bx c 0
The form ax2 bx c
where a
0
0 is called the standard form of a quadratic equation.
Examples:
x 2 5x 6 0
x2
4x
x2
T
Basic Differentiation Formulas
In the table below,
and
Derivative of a constant
Derivative of constant
multiple
Derivative of sum or
difference
(
)
(
represent differentiable functions of
We could als
Assume that x0 is a critical point of f(x)
First derivative test:
If f(x) < 0 for x< x0 but near x0 and f(x)>0 for x> x0 but near x0, then x0 is a local min.
If f(x) > 0 for x< x0 but near x0 and f(x)
EXPONENT RULES & PRACTICE
1. PRODUCT RULE: To multiply when two bases are the same, write the base and ADD the exponents.
Examples:
A.
B. 2 2 2
C.
2. QUOTIENT RULE: To divide when two bases are th
ADDING AND SUBTRACTING RATIONAL EXPRESSIONS
To Add or Subtract Two Fractions
, 0
Example 1
a) Add
Solution: a)
, 0
b) Subtract
b)
The same principles apply when adding or subtracting rational
Handout 1
1. Functions
2. Simple annual interest at a rate of r*100% invested for t years
F V = P V (1 + r t)
3. Compound annual interest at a rate of r*100% compounded annually invested for t years
F
Percentage Change
Here, I provide a discussion on percentage change and interest rate.
Lets say the price or value of an investment is Vb at the beginning of a period. The price or
value at the end of
Algebra Review
1. Laws of Exponents
2. Adding and Subtracting Rational Expressions
3. Quadratic Formula and Factoring
4. Summation Notation
5. Solving Systems of Equations
6. Solving Systems of Inequa
Handout 2
1. Eective Rate for continuously compounded annual interest
2. Denition of log
logb x = y
lnx = loge x = y
by = x
ey = x
3. Composite Functions and Inverse Functions
4. Average rate of Chang