Business Calculus – Project Greater Ed

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Functions

Functions Fundamentals 3 Topics

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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

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Graphing Lines

Finding Equations of Lines

Quadratic and Polynomial Functions 2 Topics

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Quadratic Functions and Their Graphs

Polynomials and Degree

PRAXIS: Linear, Quadratic, and Polynomial Functions

Exponential Functions 2 Topics

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Exponential Functions: What They Are, and How to Evaluate Them

Graphing (Simple) Exponential Functions

Logarithmic Functions 3 Topics

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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

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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

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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

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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

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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

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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

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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

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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

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The Power Rule for Antiderivatives

Initial Value Problems: Solving for C

The U-Substitution Method 3 Topics

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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

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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

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Finding a Function’s Average Value Using Integrals

Moving Averages

PRAXIS: Area, Continuous Accumulation, and Definite Integrals

Compound Interest and Continuous Compounding 2 Topics

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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