Question

A rectangular dog pen is to be enclosed with 20 m of fencing. The area of the dog pen, A square metres, is modelled by the function A = 10x - x^2, where x is the width, in metres. What is the width that gives maximum area? Write the answer to the nearest tenth, if necessary. A. 5 m B. 25 m C. 20 m D. 10 m

Answer 1

The correct answer is B.

Explanation:

Method 1:

A(x) = 10x - x²

A'(x) = 10 - 2x = 0

2x = 10

x = 5

A(5) = 10(5) - 5² = 50 - 25 = 25 m²

Method 2:

A = (20/4)² = 5² = 25 m²