Dual Enrollment Program: DE Course Math 1431
Math 1431 Business Calculus covers differential and integral calculus of algebraic, logarithmic, and exponential functions; applications to business and economics, such as maximum-minimum problems, marginal analysis, and exponential growth models.
Topics and Objectives
Section numbers refer to Calculus for Business, Economics, Life Sciences, and Social Sciences, 14e (Barnett, Ziegler, Byleen).
1.1 Functions
- Use points on a graph to identify input and output values
- Evaluate functions
- Find the domain of a function
- Solve applications involving functions and their graphs
1.3 Linear and Quadratic Functions
- Graph linear equations
- Work with slope, y-intercept, and the slope-intercept form of a line
- Write the equation of a line given two points
- Find the intercepts, vertex, range, and maximum or minimum value of a parabola from its graph
- Use the vertex form of a quadratic function to find information about its graph
1.5 Exponential Functions
- Graph exponential functions
- Describe transformations of the graphs of exponential functions
- Graph exponential functions
- Use properties of exponential functions to solve equations
- Solve applications involving exponential functions
1.6 Logarithmic Functions
- Evaluate logarithms
- Simplify logarithmic expressions
- Solve logarithmic and exponential equations
- Graph logarithmic functions
- Solve applications involving logarithmic functions
2.1 Introduction to Limits
- Use the graph of a function to estimate limits and function values
- Use the properties of limits to find limits algebraically
- Sketch the graph of a function using limits and function values
- Find the limit of a difference quotient
- Solve applications involving limits
2.2 Infinite Limits and Limits at Infinity
- Find infinite limits and limits at infinity using a graph
- Find limits of rational functions
- Find limits of functions at infinity
- Describe the behavior of a rational function
- Find horizontal and vertical asymptotes
- Use the properties of limits to find limits algebraically
- Solve applications involving limits and limits at infinity
2.3 Continuity
- Sketch the graph of a function using limits and function values
- Estimate function values and limits using the graph of the function
- Use the continuity properties of functions to determine where a function is continuous
- Use continuity properties to solve inequalities
- Solve applications involving continuity
2.4 The Derivative
- Find average and instantaneous rates of change
- Use the four-step process to find the derivative of a function and evaluate the derivative
- Use the graph of a function to determine whether the function is differentiable at a given x-value
- Solve applications involving derivatives and rate of change
2.5 Basic Differentiation Properties
- Use basic differentiation properties to find the derivative of a function
- Find equation of tangent lines and values of x for the line tangent to a function is horizontal
- Solve applications involving derivatives
2.7 Marginal Analysis in Business and Economics
- Find marginal cost, revenue, and profit functions
- Solve applications involving cost, revenue, and profit functions
3.1 The Constant e and Continuous Compound Interest
- Evaluate and graph continuous compound interest functions
- Solve equations and evaluate expressions with the constant e
- Graph equations with continuous compounding
- Solve applications involving e and continuous compound interest
- Determine the future value of a lump sum of money
- Solve applied problems involving compound interest
- Determine the present value of a lump sum of money
3.2 Derivatives of Exponential and Logarithmic Functions
- Find derivatives involving exponential and logarithmic functions
- Find equations of lines tangent to graphs at particular values
- Solve applications involving derivatives of exponential and logarithmic terms
3.3 Derivatives of Products and Quotients
- Find derivatives of products
- Find derivatives of quotients
- Find the equation of a tangent line to the graph of a product or quotient function
- Find the x-value at which the derivative of a function is zero
- Solve applications involving derivatives of products and quotients
3.4 The Chain Rule
- Work with composite functions
- Find derivatives of composition functions
- Find tangent lines to the graph of a composition function
- Solve applications involving derivatives that require the chain rule
3.7 Elasticity of Demand
- Find the elasticity of demand
- Determine whether demand is elastic, inelastic, or has unit elasticity
- Find values for which demand is elastic and inelastic
- Solve applications involving the elasticity of demand
4.1 First Derivatives and Graphs
- Find intervals on which functions are increasing and decreasing
- Find local extrema
- Use or create sign charts for graphs of functions
- Find critical numbers of functions
- Sketch graphs of functions
- Solve applications involving the graph of a function’s first derivative
4.2 Second Derivatives and Graphs
- Identify particular intervals of graphs of functions
- Find inflection points
- Graph function given descriptions of the first and second derivative of the function
- Find the derivative of functions
- Find inflection points and determine concavity algebraically
- Use curve sketching techniques
- Solve applications involving the graph of a function’s second derivative
4.5 Absolute Maxima and Minima
- Find absolute extrema given the graph of a function
- Find absolute extrema of a function
4.6 Optimization
- Optimize the product of two numbers
- Solve area and perimeter optimization problems
- Solve construction cost optimization problems
- Solve geometric optimization problems
- Solve maximizing revenue and profit problems
- Solve inventory control optimization problems
5.1 Antiderivatives and Indefinite Integrals
- Find indefinite integrals
- Find particular antiderivatives
- Solve applications involving antiderivatives and indefinite integrals
5.2 Integration by Substitution
- Reverse the chain rule to find indefinite integrals
- Use the method of substitution to find antiderivatives and indefinite integrals
- Find the family of all antiderivatives of a derivative
- Solve applications involving antiderivatives that require substitution
5.4 The Definite Integral
- Identify rectangles under curves
- Graph and identify areas by left and right sums
- Calculate Riemann sums
- Use properties of the definite integral
5.5 Fundamental Theorem of Calculus
- Compare changes in a function with the area under the graph of the function's derivative
- Evaluate integrals using the Fundamental Theorem of Calculus
- Find average values of functions over intervals
- Solve applications involving definite integrals and the Fundamental Theorem of Calculus
- Evaluate integrals using the Fundamental Theorem of Calculus
- Solve applications involving definite integrals and the Fundamental Theorem of Calculus
6.1 Area between Curves
- Set up a definite integral to represent a shaded area
- Find the area between two curves
6.2 Applications
- Solve continuous income stream problems
- Find the future value of a continuous income stream
- Solve consumers' and producers' surplus problems
- Find equilibrium points, the consumer surplus, and the producer surplus
Syllabus & Pacing Guide
| Name | Last Modified |
|---|---|
| S26 Math 1431 DE Syllabus.docx [docx] | 2025-12-10 |
| S26 Math 1431 DE Pacing Guide.docx [docx] | 2025-12-10 |
Course Profile
| Name | Last Modified |
|---|---|
| Math 1431 Business Calculus COURSE PROFILE 11-20-2024 [docx] | 2025-02-03 |