Suppose you have 76 feet of fencing to enclose a rectangular dog pen. The function A = 38x - x2, where x = width, gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area? Round to the nearest tenth as necessary.

width = 19 ft; area = 361 ft2

width = 38 ft; area = 760 ft2

width = 38 ft; area = 361 ft2

width = 19 ft; area = 1083 ft2

Question

Mathematics

Mathew Padilla

22 September, 12:42

Suppose you have 76 feet of fencing to enclose a rectangular dog pen. The function A = 38x - x2, where x = width, gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area? Round to the nearest tenth as necessary.

width = 19 ft; area = 361 ft2

width = 38 ft; area = 760 ft2

width = 38 ft; area = 361 ft2

width = 19 ft; area = 1083 ft2

+4

Answers (1)

Know the Answer?

Raul Serrano · Answer 1

The answer to your question is width = 19 ft; area = 361 ft²

Step-by-step explanation:

Data

A = 38x - x²

Process

1. - Find the derivative of A

A' = 38 - 2x

2. - Equal to zero

38 - 2x = 0

3. - Solve for x

38 = 2x

x = 38/2

x = 19 ft

4. - Find the area

A = 38 (19) - (19) ²

- Simplification

A = 722 - 361

-Result

A = 361 ft²