# CALCULUS FOR BUSINESS & ECONOMICS

# CALCULUS FOR BUSINESS & ECONOMICS

**Student Level:** Freshman or sophomore

**Prerequisite:** A minimum grade of C in MTH 4420 or 23 ACT math score.

**Controlling Purpose:** To provide students in the business, economics, management,
life, and social sciences

with an introduction to the calculus.

**Learner Outcomes: **Students will be introduced to optimization, and total and
average values of functions,

through limits, derivatives, and integrals, and make applications to cost,
revenue, profit, taxation, compound

interest, supply and demand, population change, and marketing.

**Evaluation KEY:**

A = All major and minor goals have been achieved and the achievement level is
considerably above

the minimum required for doing more advanced work in the same field

B = All major goals have been achieved, but the student has failed to achieve
some of the less

important goals. However, the student has progressed to the point where the
goals of work at

the next level can be easily achieved.

C = All major goals have been achieved, but many of the minor goals have not
been achieved. In

this grade range, the minimum level of proficiency represents a person who has
achieved the

major goals to the minimum amount of preparation necessary for taking more
advanced work

in the same field, but without any major handicap of inadequacy in his
background.

D = A few of the major goals have been achieved, but the student’s achievement
is so limited that

he is not well prepared to work at a more advanced level in the same field.

F = Failing, will be computed in GPA and hours attempted.

N = No instruction or training in this area.

***DENOTES OPTIONAL MATERIAL**

**Chapter 0: A PRECALCULUS REVIEW
**Outcomes: Students will review pre calculus concepts.

A | B | C | D | F | N | Demonstrate the ability to: Specific Competencies | |

*0.1 | Represent, classify, and order real numbers , use
inequalities to represent sets of real numbers, solve inequalities , and use inequalities to model and solve real-life problems. |
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*0.2 | Find the absolute values of real numbers and
understand the properties of absolute value and find the distance between two numbers on the real number line. Find the distance between two numbers on the real number line and define intervals on the real number line. |
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*0.3 | Find the midpoint of an interval and use
intervals to model and solve real-life problems. |
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*0.4 | Evaluate expressions involving exponents or
radicals, simplify expressions with exponents and find the domains of algebraic expressions. |
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*0.5 | Use special products and factorization techniques
to factor polynomials. Find the domains of radical expressions . Use synthetic division to factor polynomials of degree three or more. Use the Rational Zero Theorem to find the real zeros of polynomials. |
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*0.5 | Add and subtract rational expressions, simplify
rational expressions involving radicals and Rationalize numerators and denominators of rational expressions. |

**Chapter 1: FUNCTIONS, GRAPHS, AND LIMITS (7 Hours)
**Outcomes: Students will learn to use function applications in real-life, such as
Dow Jones industrial average, break

even analysis, linear depreciation , demand function and market equilibrium.

A | B | C | D | F | N | Demonstrate the ability to: Specific Competencies | |

*1.1 | Plot points in the Cartesian plane and find the distance between two points. | ||||||

*1.2 | Sketch the graph of an equation , and find the x- and y- intercepts . | ||||||

*1.3 | Write equations of lines and sketch the lines. | ||||||

*1.4 | Evaluate, simplify, and find inverse functions. | ||||||

*1.5 | Find the limit of a function. | ||||||

*1.6 | Discuss the continuity of a variety of functions |

**Chapter 2: DIFFERENTIATION (8 hours)
**Outcomes: Students will find limits and derivatives, and make applications to
finding marginal functions.

A | B | C | D | F | N | Demonstrate the ability to: Specific Competencies | |

*2.1 | Find the slope of a graph and calculate derivatives using the limit definition. | ||||||

*2.2 | Use the Constant Rule, Power Rule ,
Constant Multiple Rule, and Sum and Difference Rules. |
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*2.3 | Find rates of change: velocity,
marginal profit, marginal revenue, and marginal cost. |
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*2.4 | Use the Product and Quotient Rules,
Simplify derivatives and use derivatives to answer questions about real-life situations. |
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*2.5 | Use the Chain and General Power Rule
and use the rules to differentiate algebraic functions. Write derivatives in simplified form and use them to answer questions about real-life situations. |
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*2.6 | Calculate higher-order derivatives and derivatives using implicit differentiation. | ||||||

*2.7 | Find derivatives explicitly and implicitly. | ||||||

*2.8 | Solve related-rate problems and applications. |

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