MAT 1234 Calculus I Section 3.7 Part I Optimization Problems

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MAT 1234 Calculus I Section 3.7 Part I Optimization Problems

Homework HW 3.7I (due tomorrow) HW 3.7II (available today, due Thursday) The word problems tend to be long. You should start your HW early. Be sure to pay attention to the expectations in solutions.

Homework Reminders You can get help for your HW Eventually, you need to know how to do your HW on your own.

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

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.

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.

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

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

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

First Derivative Test for Absolute Extreme Values x y

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

Step 5: Make a conclusion The dimension required is …