UTPA STEM/CBI Courses/CalculusII/Applied Optimization Problems

Course Title: Calculus 1

Lecture Topic: Using the first Derivative to solve optimization Problems

Instructor: Hanan Amro

Institution:South Texas College

Backwards Design

Course Objectives

• Primary Objectives- By the next class period students will be able to:
  • Solve applied Maximum and Minimum Problems using Calculus

• Sub Objectives- The objectives will require that students be able to:
  • The student need to indentify the known and unknown for each problem.
  • The Students need to write the primary equation from the given information.
  • The students need to Determine the feasible domain of the primary equation.

• Difficulties- Students may have difficulty:
  • Some student has difficulites coming up with equation to set up the the problems
  • Derivative of trigonometric Function, and Chain Rule

• Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
  • Minimizing the cost ,Maximize the profit
  • Desiging a suit case, minimize the dimension of a poster ,Maximize the sensitivity to medicine.

Model of Knowledge

• Concept Map
  • Set up the equations from known and unkown informations
  • Determine the Crictical Values
  • Set the first derivative equal to zero
  • Detemine the Local Extrema (Maximum and Minimum)
• Content Priorities
  • Enduring Understanding
    • text
    • text
    • text
  • Important to Do and Know
    • First Derivative Test for Absolute Extrema

Let I be the interval of all possible optimal values of f(x) and further suppose that f(x)is continuous on I , except possibly at the endpoints. Finally suppose that x = c is a critical point of and that c is in the interval I. If we restrict x to values from I (i.e. we only consider possible optimal values of the function) then,

• • • text
    • text
  • Worth Being Familiar with
    • text
    • text
    • text

Assessment of Learning

• Formative Assessment
  • In Class (groups)
    • text
    • text
  • Homework (individual)
    • text
    • text
• Summative Assessment
  • In class quizz over the subject
  • Test involve topic similar to the challenge

Legacy Cycle

OBJECTIVE

By the next class period, students will be able to:

• Covert the word problem into mathematical equation
• solve the equation using first derivative test.

The objectives will require that students be able to:

• text
• text

THE CHALLENGE

A farmer plan to fence a rectangular pasture adjacent the river see the diagram. The pasture must contain 245,000 square meters in order to provide enough grass for the herd. What dimensions will require the least amount of fencing if no fencing is needed along the river

.

GENERATE IDEAS

text

MULTIPLE PERSPECTIVES

text

RESEARCH & REVISE

text

TEST YOUR METTLE

text

GO PUBLIC

text

Pre-Lesson Quiz

1. question
2. question
3. question
4. question
5. question
6. question
7. question
8. question
9. question
10. question
11. question
12. question
13. question
14. question
15. question
16. question
17. question
18. question
19. question
20. question

Test Your Mettle Quiz

1. Suppose that c(x) = x³ -20x² +20,000x is the cost of the manufacturing x items. Find the level

of a production level that will minimize the average cost of making x items.

1. A rectanluar plot of farmland will be bounded on one side by the river and on the other three sides by

a single-strand electric fence.  With 800 m of wire at disposal, what is the
largest area you can enclose, and what are its dimension?

1. We want to construct a box with a square base and we only have 10 m2 of material to use

in construction of the box.  Assuming that all the material is used in the construction 
 process determine the maximum volume that the box can have.

1. question
2. question
3. question
4. question
5. question
6. question
7. question
8. question
9. question
10. question
11. question
12. question
13. question
14. question