Unformatted text preview: Calculus Project 1 Designing an Environmentally Friendly Package Introduction You have been hired by the CEO of a major company to design the packaging for its newest cereal. The CEO takes environmental issues very seriously and wants to make sure that the box that you design uses as little material as possible. Objectives: You will be able to calculate the derivative of a function using the product rule You will be able to calculate the derivative of a function using the quotient rule You will be able utilize derivatives to analyze optimization problems. You will be able to show multiple representations of a mathematical solution (algebraic/analytical, numeric, graphical, written english) Specifications for the packaging The cereal must be packaged in a rectangular box. The base must be ______ times the width. (number to be assigned by teacher) The volume of the box must hold exactly _____ inches3. (number to be assigned by teacher) The box must use the least amount of cardboard (minimize the surface area) to save money. You must write a clear step by step description of your design process supported by functions, derivatives, graphs, and data tables to convince the CEO that your design is the most efficient use of material. Calculus Project 1: Design an environmentally friendly package Name, Date, Class, and Title 4 3 All of Name, Date, Class, and Most of Name, Date, Class, and Project title are written at Project title are clearly top of the paper. written at top of the paper. A mostly clear step by step A very clear step by step description of your design description of your design strategy is included. All major strategy is included. Most, but not all, major steps are steps are explained clearly and precisely. Key explained clearly and mathematical terms are used precisely. Key mathematical appropriately. terms are used appropriately. A very clear algebraic solution A mostly clear algebraic solution to your design to your design strategy is strategy is included. included. This means that proper This means that proper formulas and functions are formulas and equations are correctly written and solved. correctly written and solved. All steps are neatly shown Most, but not all, steps are until a conclusion is found. neatly shown until a No mistakes. conclusion is found. Only one or two mistakes. A mostly clear data table shows the behavior of all key functions and derivatives that support your design strategy. Some of the most important data values are highlighted and their significance to your solution is described with few mistakes. Columns are labeled with correct units. A very clear data table shows the behavior of all key functions and derivatives that support your design strategy. All of the most important data values are highlighted and their significance to your solution is accurately described. Columns are labeled with correct units. Written Description of your process 2 Some of Name, Date, Class, and Project title are written at top of the paper. A step by step description of your design strategy is included. Some, but not all, major steps are explained. Little or improper use of mathematical terms. An algebraic solution to your design strategy is included. This means that proper formulas and equations are correctly written and solved. Some steps are shown, but some are skipped making the process difficult to follow. Three or four mistakes. 1 None of Name, Date, Class, and Project title are written at top of the paper. A step by step description of your design strategy is not included or lacks most major steps. Little or no use of mathematical terms. Algebraic Representation of your process An algebraic solution to your design strategy is not included or has many mistakes. Very few or no steps are shown making the process difficult to follow. More than four mistakes. Numerical Representation of your process (Data Table of functions and derivatives) A data table shows the No data table included behavior of some, but not all, key functions and derivatives. Few or none of the most important data values are highlighted. Incorrect or no use of labels and units. Graphical Representation of your process Use of calculus concepts Actual Cereal Box On Time 4 3 Graphs show the behavior of Very clear graphs show the behavior of all key functions all or most key functions and and derivatives that support derivatives that support your your design strategy. All of design strategy. Most of the the important points on the important points on the curves are highlighted and curves are highlighted and their significance to your their significance to your solution is clearly described. solution is described with few All axis are properly labeled mistakes. Most axis are and have correct units. properly labeled and have correct units. Appropriate and accurate Appropriate and accurate application and interpretation application and interpretation of derivatives is an important of derivatives is part of your design solution. These part of your design solution. concepts are incorporated in These concepts are clearly incorporated in your written, your written, algebraic, algebraic, numeric, and numeric, and graphical graphical representations. representations with some mistakes. You have constructed the full You have constructed full size cereal box that is mostly size cereal box that is accurate to your calculations. accurate to your calculations All key dimensions of the box with one or two mistakes. are clearly labeled with units Most key dimensions of the (length, width, height, volume box are labeled with units and surface area) (length, width, height, volume and surface area) The completed project is delivered within one day after the due date: Start of class on Tuesday December 9. The completed project is delivered on or before the due date: Start of class on Tuesday December 9. 2 Graphs show the behavior of some functions and derivatives. Few of the important points on the curves are highlighted and their significance to your solution is not made clear. Axis are not properly labeled. 1 Graphs are not included or have numerous major mistakes. Appropriate and accurate application and interpretation of derivatives is part of your design solution. These concepts are incorporated in your some of your written, algebraic, numeric, and graphical representations with many mistakes. You have constructed the cereal box that is somewhat accurate to your calculations with three or four mistakes. Some key dimensions of the box are labeled with units (length, width, height, volume and surface area) The completed project is delivered within three days after the due date: Start of class on Tuesday December 9. Appropriate and accurate application and interpretation of derivatives is not part of your design solution or contains many mistakes. You have not constructed the cereal box or you have more than four mistakes. The completed project is delivered more than three days after the due date: Start of class on Tuesday December 9 ...
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This note was uploaded on 02/03/2012 for the course MATH 101 taught by Professor Lee during the Spring '11 term at International Institute for Higher Education.
 Spring '11
 Lee
 Calculus

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