## Math 150 Lecture 002 - Sixth Homework Assignment

This assignment is related to

### For discussion at recitation on T Oct. 20, and Th Oct. 22.

#### MAPLE:

• Go through the worked Sample Problems for Chapter 4. This material is found on pages 139 - 140 of the Lab Manual. I suggest that you first try to do the problems using MAPLE on your own. Then compare your solutions with those in the Lab Manual.
• Work through Demonstration #5.

•  MAPLE ASSIGNMENT #1 (Due on Monday, October 26)
• RULES:
• You may work on these problems with other students in Math 150, and you may seek guidance (not solutions) from your TA's or other normal sources of Math Help. However, once you understand how to use MAPLE to solve these problems, you must create your own version of the solutions. The paper that you turn must be your own work in your own words -- not what someone else is able to do for you.
• Your paper should be the print-out of a MAPLE session including the output of all MAPLE commands.
• Note that you can include lines of pure text . You must add notes between your MAPLE commands that explain the steps you are taking. Sequences of MAPLE commands with no notes will receive no credit.
• The first line of text must include your name, recitation (one of: 211 - 218), and TA name.
• Do the following two problems
• Problem 11 on page 184 of your Lab Manual (Section on "Derivative Problems.")
• Consider the function x^4-5*x^3+3*x-7 on the interval from -1 to +4.
• Find the critical points.
• Find the maximum and minimum on this interval.
• Find the inflection points.
• Give a good plot of the function on this interval. (You will have to experiment with restricting the "y" range.)

READING: Chapter 4 Sections 6 and 7. These sections cover one of the most important applications of the differential calculus -- the use of derivatives in solving optimization problems. This material should receive your careful attention!

Solution Error: Problem 23, section 4.7. The minimum for this problem does not occur at an integer point. The text concludes correctly that one has to have an integer number of orders. The integer nearest the minimum point is 45. From this it follows that the number ordered each time is 2,000,000/45 (i.e. 44445 (the next higher integer) -- not 44,721 as given in the answer section of the text).

CORE PROBLEMS: Write up, for your own record, solutions to the Core Problems for Chapter 4 sections 6 and 7.

ADDITIONAL PROBLEMS: Work as many of the odd numbered review exercises for Chapter 4 as you can.

OLD FINAL EXAM PROBLEMS: Final Exams for the past eight semesters are included at the back of your Math 150/151 Lab Manual. For this week's assignment you should work the following problems from the old final exams:

 Fall 1996: #4, 23 Spring 1997: #11, 20 Fall 1997: #9 Spring 1998: none this time

For the directory of homework assignments, see HOMEWORK.