Business Calculus

Functions
Functions Fundamentals
3 Topics
Functions and Their Representations: Potato Diagrams, Tables, Graphs, and Rules
Drawing Graphs by Point-Plotting
Function Domains, Codomains, and Ranges
PRAXIS: Functions Fundamentals
Linear Functions
2 Topics
Graphing Lines
Finding Equations of Lines
Quadratic and Polynomial Functions
2 Topics
Quadratic Functions and Their Graphs
Polynomials and Degree
PRAXIS: Linear, Quadratic, and Polynomial Functions
Exponential Functions
2 Topics
Exponential Functions: What They Are, and How to Evaluate Them
Graphing (Simple) Exponential Functions
Logarithmic Functions
3 Topics
Logarithmic Functions: What They Are, and How to Evaluate Them
Change-of-Base Formula and Computing Logs with a Calculator
Graphing (Simple) Logarithmic Functions
Constructing New Functions From Old Ones
4 Topics
Basic Function Arithmetic Using Function Rules, and Numerical Substitutions
Function Arithmetic: Using Tables to Evaluate Various Combinations of Functions at a Given Value
Function Arithmetic: Using Graphs to Evaluate Various Combinations of Functions at a Given Value
Piecewise Functions
PRAXIS: Exponential Functions, Logarithms, and Building New Functions From Old
Solving Equations with Functions
3 Topics
The Guess and Check Method for Solving Equations
Solving Equations Using Graphs
Algebraically Solving Equations
PRAXIS: Solving Functional Equations
Limits and Derivatives
Limits – An Overview
Left, Right, and Two-Sided Limits
3 Topics
Finding Limits Using Graphs
Guessing Limits Using Tables
Finding Limits Of Polynomials
PRAXIS: Limits
The Derivative as a Limit of an Average Rate of Change
4 Topics
Average Rates of Change
Finding Derivatives as a Limit of an Average Rate of Change
The h-Form of the Derivative and Finding Tangent Lines
The Derivative as a Function
PRAXIS: Derivatives Basics
Basic Derivative Rules
6 Topics
Deriving Polynomials Using the Power Rule and Simple Derivative Properties
Derivatives of Exponential Functions of the Form \(c\cdot e^x\)
Product Rule
Quotient Rule
Chain Rule
Derivatives of Logarithmic Functions
Finding Derivatives Using Several Different Rules
PRAXIS: Derivative Rules
Applications of Differentiation
Extrema: Finding Minima and Maxima
3 Topics
Finding Extrema by Graphing
First Derivative Test for Finding Local Mins and Maxes
First Derivative Test and Global Mins and Maxes
PRAXIS: Extrema
Concavity, Inflection Points, and the Second Derivative Test
3 Topics
Concavity and Inflection Points With Graphs
Concavity and Inflection Points Without Graphs
Second Derivative Test for Classifying Critical Points
PRAXIS: Concavity, Inflection Points, and Second Derivative Test
Optimization Applications
PRAXIS: Optimization Applications
Integration
Antiderivatives and Basic Rules for Such
2 Topics
The Power Rule for Antiderivatives
Initial Value Problems: Solving for C
The U-Substitution Method
3 Topics
How the Method Works
Using U-Sub with Exponential Functions
Antiderivatives that Result in Logarithms
PRAXIS: Antiderivatives
Area, Continuous Accumulation, and Definite Integrals
3 Topics
What Integrals Are and the Fundamental Theorem of Calculus
Computing Integrals Involving U-Substitution
Areas Between Curves
Average Value of a Function, and Moving Averages
2 Topics
Finding a Function’s Average Value Using Integrals
Moving Averages
PRAXIS: Area, Continuous Accumulation, and Definite Integrals
Compound Interest and Continuous Compounding
2 Topics
Compound Interest – Multiplying Your Money
The Natural Exponential Function and Continuous Compounding
Future Value of Income Streams
PRAXIS: Applications of Integration – Compound Interest and Future Value of Income Streams
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Exponential Functions

Business Calculus Exponential Functions

In what follows…

We will be talking about a class of functions that are NOT polynomials in any way, namely exponential functions.

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