# CALCULUS FOR BUSINESS & ECONOMICS

**Chapter 3: APPLICATIONS OF THE DERIVATIVE (8 hours)
**Outcomes: Students will make application of derivatives to curve sketching, and
maximizing cost, revenue, and profit

in competitive and monopolistic markets.

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

*3.1 | Find the open intervals on which a function is increasing or decreasing. | ||||||

*3.2 | Recognize the occurrence of relative
extrema of functions and use the First- Derivative Test to find the relative extrema of functions. Find absolute extrema of continuous functions on a closed interval and minimum and maximum values of real -life models and interpret the results in context. |
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*3.3 | Determine the concavity and points of inflection of a graph. | ||||||

*3.4 | Solve real -life optimization problems. | ||||||

*3.5 | Solve business and economics
optimization problems. Find the price elasticity of demand for demand functions and recognize basic business terms and formulas . |
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*3.6 | Determine vertical and horizontal asymptotes of a graph. | ||||||

*3.7 | Analyze the graphs of functions and
recognize the graphs of simple polynomial functions. |
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*3.8 | Use calculus to analyze the shape of the graph of a function. |

**Chapter 4: EXPONENTIAL AND LOGARITHMIC FUNCTIONS (8 hours)
**Outcomes: Students will explore applications in compound interest, growth and
decay, and management sciences

using exponential and logarithmic.

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

*4.1 *4.2 |
Graph the exponential function f(x) =
a^{X} and graph the natural exponentialfunction f(x) = e ^{X} |
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*4.3 | Calculate derivatives of exponential functions. | ||||||

*4.4 | Graph the logarithmic function f(x) =
In x and use it to solve exponential and logarithmic equations . |
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*4.5 | Calculate the derivatives of logarithmic functions | ||||||

*4.6 | Solve exponential growth and decay applications. |

**Chapter 5: INTEGRATION AND ITS APPLICATIONS (8 hours)
**Outcomes: Students will learn to use integration applications in real life such
as demand function, vertical motion,

marginal propensity to consume, annuity, capital accumulation, consumer and producer surpluses and

Lorenz Curve .

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

*5.1 | Find the antiderivative F of a function – that is, F'(x) = f(x) | ||||||

*5.2 *5.3 |
Use the General Power Rule ,
Exponential Rule, and Log Rule to calculate antiderivatives. |
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*5.4 *5.5 |
Evaluate definite integrals and apply
the Fundamental Theorem of Calculus to find the area bounded by two graphs . |
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*5.6 | Use the Midpoint Rule to approximate
definite integrals and use a symbolic integration utility to approximate definite integrals. |
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*5.7 | Use integration to find the volume of a solid of revolution. |

**Chapter 6: TECHNIQUES OF INTEGRATION (8 hours)
**Outcomes: Students will learn to use the various integration techniques in many
applications in real life such as

present and future value, health, consumer and producer surpluses, surveying and capitalized cost.

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

*6.1 | Find indefinite and definite integrals using integration by substitution . | ||||||

*6.2 | Evaluate integrals by parts, by using
partial fractions, and by using a table of integrals. Find the present value of future income. |
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*6.3 | Use partial fractions to find
indefinite integrals. Use logistic growth functions to model real-life situations. |
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*6.4 | Use integration tables, reduction
formulas , and complete the square to find indefinite integrals. |
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*6.5 | Use the Trapezoidal Rule and Simpson’s Rule to approximate definite integrals. | ||||||

*6.6 | Evaluate improper integrals with
infinite limits of integration and with infinite integrands. |

**Text Book:** Contact the Bookstore for current textbook information.

**References:** None

**Materials/Equip required: **This course requires that the student furnish their
own TI-83 or TI-83 PLUS

graphing calculator.

**Attendance Policy: **Students should adhere to the attendance policy discussed on
the first day of class.

**Grading Policy:** Grading may vary according to the instructor.

**Max. Class Size:** 25

**Catalog Description:** MTH4432 CALCULUS FOR BUSINESS AND ECONOMICS. 3 hrs. An

introduction to differentiation and integration with applications to analytic
geometry, business and

economics. This course requires that the student furnish their own TI-83 or
TI-83 PLUS graphing calculator.

Prerequisites: Minimum grade of C in MTH 4420 or a 23 ACT math score or
satisfactory course placement

assessment scores.

**Refer to the following policies:**

402.00 Academic Code of Conduct

263.00 Student Appeal of Course Grades

403.00 Student Code of Conduct

**Disability Services Program:**

Cowley College, in recognition of state and federal laws , will accommodate a
student with a

documented disability. If a student has a disability which may impact work in
this class which requires

accommodations, contact the Disability Services Coordinator.

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