1. MAT 1221 Survey of Calculus Section 3.4 Optimization Problems http://myhome.spu.edu/lauw

2. Expectations Formally answer the problem in full sentence with the expected information Do not include information unrelated to the problem

3. Reading Read 4.3 for bonus points

4. Homework WebAssign HW 3.4 Review the examples in class carefully Do your HW ASAP

5. Preview If we need to find absolute max/min, the closed interval method is the only method we know so far. It does not work if the interval is not closed. Introduce a new method if we have one and only one critical number.

6. Example 1 A box with a square base and open top must have a volume of 32,000 cm 3. Find the dimensions of the box that minimize the amount of the material used.

7. Step 1: Draw a diagram. A box with a square base and open top must have a volume of 32,000 cm 3. Find the dimensions of the box that minimize the amount of the material used.

8. Step 2: Define the variables and the function we need to optimize

9. Step 3: Simplify the function and state the range of the variable

10. Example 1 V= 32,000 cm 3 Minimize the surface area x h

11. First Derivative Test for Absolute Extreme Values x y

12. Step 4: Use the appropriate tests to find the optimal value

13. Step 5: Make a conclusion The dimensions required are …

14. Expectations

15. Example 2

16. Step 1: Draw a diagram.

17. Step 2: Define the variables and the function we need to optimize

18. Step 3: Simplify the function and state the range of the variable

19. Step 4: Use the appropriate tests to find the optimal value

20. Step 5: Make a conclusion The required points are …

21. Expectations