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1.         use methods of algebra and calculus to analyze the graph of the function

 

                         

 

            Include all of the following in your analysis:

 

            a) the domain

b) intercepts

c) equations of asymptotes (both vertical and horizontal)

d) relative extrema (be sure to provide all derivatives, identify critical numbers,

     and show the test for those values – naming the test that you are using.)

g) intervals where the graph is concave up and where it is concave down (be sure to include the vertical asymptotes in your intervals.)

h) provide computer-generated graphs of your function that illustrate all of the

    key points that you have listed. You may need to provide more than one graph.

    2) Graph showing curve, critical points, and intervals where the function is 

        increasing or decreasing:

           

    3) Graph showing curve, inflection points, and concavity:

2.         A paper cup is to be designed in the shape of a right circular cone. It must have a capacity of 12 fluid ounces of soft drink but it must use a minimum amount of material in its construction. What should the dimensions of this paper cup be and how much material is needed for its construction.

 

            Note: In solving this problem, you must:

 

            a. Clearly explain how you obtained the function to be minimized. Be sure your variables are clearly defined and it is very clear how you took all the information given and constructed your function. Include the domain of the function. You will need to know the formula for the volume of a cone and for its lateral surface. You will also need to know that 1 fluid ounce is approximately 1.80469 cubic inches.

 

            b. Use this function to answer the question. (You will need to compute derivatives and find and test critical values.) Carefully explain all the steps you take.

 

            c. Write a clear answer to the problem.

 

 

 

  • 9 years ago
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