LSU College Readiness Program s2

LSU College Readiness Program COURSE PROFILE

COURSE NAME LSU Math 1431 Business Calculus (1 semester) COMMON COURSE NUMBER CMAT 2103 Applied Calculus PRIMARY ONLINE Calculus for Business, Economics, Life, and Social CONTENT SOURCE Sciences, 12e, MyMathLab Barnett, Ziegler, Byleen COURSE/UNIT CREDIT ½ Carnegie Unit GRADE(S) 11 or 12 PREREQUISITE(S) Math 1021 or MACT min 25

CHAPTERS 1 – Linear Equations and Graphs 5 – Graphing and Optimization 2 – Functions and Graphs 6 – Integration 3 – Limits and the Derivative 7 – Additional Integration 4 – Additional Derivative Topics

SECTION NAMES (NUMBER OF EXERCISES) AND LEARNING OBJECTIVES CHAPTER 1: Linear Equations and Graphs 1.2 Graphs and Lines (29) Determine whether the slope of a line is positive, negative, zero, or undefined Graph equations Recognize the placement of slope and y-intercept in the slope-intercept form of a line Use the graph of a line to write its equation Find the slope of an equation written in standard form Find the x- and y-intercepts of the graph of a line Write equations for vertical and horizontal lines Write the equation of a line given the slope and a point Write the equation of a line given two points Solve applications CHAPTER 2: Functions and Graphs 2.1 Functions (19) Use points on a graph to identify input and output values Evaluate functions Find the domain of a function Solve applications 2.5 Exponential Functions (12) Graph exponential functions Use properties of exponential functions to solve equations Solve equations involving exponentials Solve applications CHAPTER 3: Limits and the Derivative 3.1 Introduction to Limits (26) 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 application problems 3.2 Infinite Limits and Limits at Infinity (32) 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 Evaluate limits using properties of limits Solve application problems 3.3 Continuity (19) Sketch the graph of a function using limits and function values Use the definition of continuity Use continuity properties of functions Use continuity properties to solve inequalities Solve application problems 3.4 The Derivative (18) Find average and instantaneous rates of change Use the four-step process to find the derivative of a function Find average and instantaneous velocities Find the slopes of secant and tangent lines Determine where a function is differentiable or nondifferentiable Solve application problems 3.5 Basic Differentiation Property (34) Use basic differentiation properties Differentiate a constant or a constant times a function Find slopes of tangent lines Find slopes of tangent lines and values of x where the tangent line is horizontal Solve application problems 3.7 Marginal Analysis (14) Find marginal cost, revenue, and profit functions Solve application problems CHAPTER 4: Additional Derivative Topics 4.1 Continuous Compound Interest (14) Solve equations and evaluate expressions with the constant e Graph equations with continuous compounding Solve applications Determine the future value of a lump sum of money Solve continuous compounding problems Solve applied problems involving compound interest Determine the present value of a lump sum of money 4.2 Derivatives of Exponential and Logarithmic Functions (14) Find derivatives involving exponential and logarithmic functions Find equations of lines tangent to graphs at particular values Solve application problems 4.3 Derivatives of Products and Quotients (32) Find derivatives of products Differentiate using the product rule Use the product rule Find derivatives of quotients Use the quotient rule Solve application problems 4.4 The Chain Rule (32) Work with composite functions Use the general power rule to find derivatives Use the chain rule to find derivatives Solve application problems 4.7 Elasticity of Demand (9) 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 application problems CHAPTER 5: Graphing and Optimization 5.1 First Derivatives and Graphs (30) Find intervals on which functions are increasing and decreasing Find local extrema Create sign charts for graphs of functions Find critical values of functions Sketch graphs of functions Solve application problems 5.2 Second Derivatives and Graphs (21) Identify particular intervals of graphs of functions Find inflection points Graph function given descriptions Find inflection points and determine concavity algebraically Use curve sketching techniques Solve application problems 5.5 Absolute Maxima and Minima (18) Find absolute extrema of a function 5.6a Optimization, Geometric Applications (11) Optimize the product of two numbers Solve area and perimeter optimization problems Solve construction cost optimization problems Solve geometric optimization problems 5.6b Optimization, Business Applications (10) Solve maximizing revenue and profit problems Solve inventory control optimization problems CHAPTER 6: Integration 6.1 Antiderivatives and Indefinite Integral (30) Identify antiderivatives and indefinite integrals Find particular antiderivatives Solve application problems 6.2 Integration by Substitution (20) Reverse the chain rule to find indefinite integrals Use the method of substitution to find antiderivatives and indefinite integrals Solve application problems 6.4 The Definite Integral (14) Identify rectangles under curves Graph and identify areas by left and right sums Calculate Riemann sums Use properties of the definite integral 6.5a Fundamental Theorem of Calculus, Basic (20) Compare changes in a function with the area under the graph of the function's derivative Use the Fundamental Theorem of Calculus to calculate the definite integral of a function Solve application problems Determine the average value of functions Find average values of functions over intervals 6.5b Fundamental Theorem of Calculus, Substitution (13) Evaluate integrals using the Fundamental Theorem of Calculus Evaluate definite integrals Evaluate integrals using substitution Solve application problems CHAPTER 7: Additional Integration 7.1 Area between Curves (23) Set up a definite integral to represent a shaded area Find the area between two curves Find the area under the graphs of nonnegative functions over closed intervals 7.2 Applications (13) 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