3.6: Optimization Problems

� Guidelines for Optimization Problems

1. Read the problem carefully, more than once.

2. Sketch a picture or diagram if appropriate.

3. Write down any information given from the problem, and any other information that may

relate to the problem (ex: formulas).

4. Determine which variable is to be maximized or minimized, and express this variable as a

function of one of the other variables.

5. Find the critical values of the function from step 4.

6. Determine the extrema using a first derivative number line or the second derivative test.

Check the endpoints whenever appropriate.

Calculus: LUPO

3.6 Day 1 Notes

Name: ___________________________________

1) You wish to build an aquarium which holds 36 cubic feet of water. You want the length to be twice the width. What dimensions would require the least amount of glass?

2) In the aquarium above, suppose glass for the sides cost $4 per square foot and glass for the bottom costs $10 per square foot. Provided the volume is 36 cubic feet and the length is twice the width, what dimensions would minimize the cost?

HW: pg 313: 7, 17