Dual Enrollment Program DE Course: Math 1431 Business Calculus

• 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

• 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

• 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

• Evaluate logarithms
• Simplify logarithmic expressions
• Solve logarithmic and exponential equations
• Graph logarithmic functions
• Solve applications involving logarithmic functions

Chapter 2: Limits and the Derivative

• 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

• 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

• 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

• 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

• 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

• Find marginal cost, revenue, and profit functions
• Solve applications involving cost, revenue, and profit functions

Chapter 3: Additional Derivative Topics

• 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

• 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

• 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

• 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

• 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

Chapter 4: Graphing and Optimization

• 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

• 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

• Find absolute extrema given the graph of a function
• Find absolute extrema of a function

• 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

Chapter 5: Integration

• Find indefinite integrals
• Find particular antiderivatives
• Solve applications involving antiderivatives and indefinite integrals

• 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

• Identify rectangles under curves
• Graph and identify areas by left and right sums
• Calculate Riemann sums
• Use properties of the definite integral

• 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

Chapter 6: Additional Integration Topics

• Set up a definite integral to represent a shaded area
• Find the area between two curves

• 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