Calculus I Optimization Problems Handout

Calculus I Optimization Problems Handout - Examples 1#23...

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Calculus I Optimization Problems Steps to solve: (1) Whenever possible draw and label a picture. (2) Write a formula for whatever quantity is to be maximized or minimized. (3) Use information given in the problem to write the quantity in step (2) in terms of only one variable and simplify the formula as much as possible. (4) Take the derivative and find the critical numbers. (5) Verify that that your critical numbers give you max or min that you wanted using either the 1 st or 2 nd Derivative Test. (6) Make sure you answer the question.
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Unformatted text preview: Examples: 1. #23, p.266 in your text: A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window. Find the dimensions of a Norman window of maximum area if the total perimeter is 16 feet. 2. A right circular cylinder is to be designed to hold 22 cubic inches of a soft drink. The cost for the material for the top and bottom of the can is twice the cost for the material of the sides. Find the radius that minimizes cost....
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