Additional Notes Flashcards
(42 cards)
How to calculate extreme points and inflection points
Step 1: 1st, 2nd, 3rd derivative
Step 2: find f’(x)=0
Step 3: plug-in f’(x) = 0 points to OG to find value pair (x/y) extremas
Step 4: plug-in f’(x) point to f”(x) function to find out if min or max
Inflection points
Step 1: find f”(x)=0 then plug in points to OG function to find value pair pf inflection points (x/y)
Step 2: confirm- if f”’(x) is NOT 0, then it’s an inflection point
What is lnx=a
e^a
What is log (1)
0
How to know if polynomial function is local or global
Step 1: check degree of function:
If even, then:
+ co-efficient = global min/ local max
- co-efficient= global max/ local min
If odd, then:
only LOCAL min/max
What is your goal in optimization
Minimum: Cost
Maximum: Revenue & Production
How to get profit function?
Revenue - Cost
What is business math?
Business math is the application of mathematical methods to solve business and economic problems. It uses tools such as functions, differential calculus, optimization and financial math. Business math can help analyze a company’s profit, revenue and costs. Additionally, it can help optimize production and pricing strategies as well as aid in making data-driven decisions.
For example it can calculate the equilibrium point for supply and demand, break-even points in production and economies of scale.
Business math is an essential tool that can help quantify and systemize business processes in leading companies to success.
What do you need to watch out for when doing partial derivatives
The + and - signs before the variables
What is the derivative of e^y with respect to y
also e^y
What is annuity in tagalog?
Hulugan
What is the difference between a derivative and differential?
Derivative: tells you the rate of change (slope)
Differential: tells you about the small changes in the variable themselves
What is the difference between partial derivative and partial differential?
Partial derivative (dz/dx or fx): tells you how fast z changes when only x changes and y stays the same
Partial differential (dz): tells you the small actual change in z. Both x and y have small changes (dx and dy)
How to solve for zeros in a rational function
1) Set nominator =0
2) Make sure not to use values that make denominator zero when you do arithmetic, in your answers
How to know if definite or indefinite integral
Definite: with upper and lower interval limit at integration sign
Indefinite: no numbers at integration sign
What are the differences between differential quotient, derivative and differentiation??
Differential quotient: the formula to find average rate of change
Derivative: the exact slope at a point (limit)
Differentiation: the action of finding the derivative
What does PITA stand for???
P - Outstanding debt
I - Interest amount
T - Repayment rate
A - Annuity
What is an inflection point?
Where the curve changes richtung
What should you know about the shape of a rational function?
It is a hyperbola
It has asymptotes and the 2 functions mirror each other
What is the most important thing to remember about rational functions?
It shows if a company produces economy of scale!!!
If you have economy of scale what business decisions are justified?
Mergers
Market domination
What do you do in a problem if you see a demand and a supply function?
Just set to equal to get market equilibrium
The x is quantity
The y is price
What must you always remember when solving square root equations?
There are always TWO answers
+ and -
What are the rules for inflection point?
f “(x) = 0
f”’ (x) in NOT 0
What are the rules for extreme point and min/max
Extreme point :
f ‘(x) = 0
Min/max:
Use extreme points in f”(x)
Determine if < or > 0
