AP Calculus ABmediummcq1 pt

A farmer has 400 feet of fencing to enclose a rectangular field that borders a river, so fencing is needed on only three sides. What is the maximum possible area of the field?

A.10,000 ft210{,}000 \text{ ft}^2
B.40,000 ft240{,}000 \text{ ft}^2
C.80,000 ft280{,}000 \text{ ft}^2
D.20,000 ft220{,}000 \text{ ft}^2

Explanation

Core Concept

If xx is the width, the length is 4002x400-2x and A=x(4002x)A=x(400-2x). A=4004x=0A'=400-4x=0 gives x=100x=100, so the maximum area is 100×200=20,000 ft2100\times200=20{,}000\text{ ft}^2.

Correct Answer

D20,000 ft220{,}000 \text{ ft}^2

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