Question

In each box is a step in the process of solving a max/min problem like the one in Question 8. Number these steps in order (1-8) to generate a useful checklist. The first one is done for you. Evaluate the y-values of the critical points and endpoints by plugging them into the function being optimized. The largest y- value is the global maximum, and the smallest y-value is the global minimum. Use the constraint equation to write a new formula for the quantity being optimized that is a function of one variable. Assign variables to quantities that change. 1. Make a drawing. Find the derivative and then the critical points of the function being optimized. Identify the constraint equation. Identify the endpoints, that is, the domain of the function being optimized. Identify and write down a formula for the quantity that is being optimized.

Answer 1

The steps are numbered below

Explanation:

To solve a maximum/minimum problem, the steps are as follows.

1. Make a drawing.

2. Assign variables to quantities that change.

3. Identify and write down a formula for the quantity that is being optimized.

4. Identify the endpoints, that is, the domain of the function being optimized.

5. Identify the constraint equation.

6. Use the constraint equation to write a new formula for the quantity being optimized that is a function of one variable.

7. Find the derivative and then the critical points of the function being optimized.

8. Evaluate the y-values of the critical points and endpoints by plugging them into the function being optimized. The largest y- value is the global maximum, and the smallest y-value is the global minimum.