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The top and bottom margins of a poster are 6 ft and the side margins are each 8 ft. If the area of printed material on the poster is fixed at 390 square ft, find the dimensions of the poster with the smallest area. printed material Part 1: Let x be the width and y the height of the printed material. Find the area of the printed material as a function of x and y. a(x, y) xy Part 2: Find the total area of this poster. Part 3: Find y as a function of x, using the given value of the area of the printed material. Part 4: Rewrite the total area of this poster as a function of x. Part 5: Find the derivative of the total area of this poster as a function of x. Part 6: Find the x and y values that minimize the total area of the poster. ft. ft. What test did you use to check whether your answer yields a minimum? First derivative test Remark: instructor could ask for a written explanation, if desired. Part 7: Find the dimensions of the poster with the smallest area.

The top and bottom margins of a poster are 6 ft and the side margins are each 8 ft. If the area of printed material on the poster is fixed at 390 square ft, find the dimensions of the poster with the smallest area. printed material Part 1: Let x be the width and y the height of the printed material. Find the area of the printed material as a function of x and y. a(x, y) xy Part 2: Find the total area of this poster. Part 3: Find y as a function of x, using the given value of the area of the printed material. Part 4: Rewrite the total area of this poster as a function of x. Part 5: Find the derivative of the total area of this poster as a function of x. Part 6: Find the x and y values that minimize the total area of the poster. ft. ft. What test did you use to check whether your answer yields a minimum? First derivative test Remark: instructor could ask for a written explanation, if desired. Part 7: Find the dimensions of the poster with the smallest area.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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The top and bottom margins of a poster are 6 ft and the side margins are each 8 ft. If the area of printed material on the poster is fixed at 390 square ft, find the dimensions of the poster with the smallest area. printed material Part 1: Let x be the width and y the height of the printed material. Find the area of the printed material as a function of x and y. a(x, y) xy Part 2: Find the total area of this poster. Part 3: Find y as a function of x, using the given value of the area of the printed material. Part 4: Rewrite the total area of this poster as a function of x. Part 5: Find the derivative of the total area of this poster as a function of x. Part 6: Find the x and y values that minimize the total area of the poster. ft. ft. What test did you use to check whether your answer yields a minimum? First derivative test Remark: instructor could ask for a written explanation, if desired. Part 7: Find the dimensions of the poster with the smallest area.
Transcribed Image Text:The top and bottom margins of a poster are 6 ft and the side margins are each 8 ft. If the area of printed material on the poster is fixed at 390 square ft, find the dimensions of the poster with the smallest area. printed material Part 1: Let x be the width and y the height of the printed material. Find the area of the printed material as a function of x and y. a(x, y) xy Part 2: Find the total area of this poster. Part 3: Find y as a function of x, using the given value of the area of the printed material. Part 4: Rewrite the total area of this poster as a function of x. Part 5: Find the derivative of the total area of this poster as a function of x. Part 6: Find the x and y values that minimize the total area of the poster. ft. ft. What test did you use to check whether your answer yields a minimum? First derivative test Remark: instructor could ask for a written explanation, if desired. Part 7: Find the dimensions of the poster with the smallest area.
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