A rectangle has its base on the -axis and its upper two vertices on the parabola , symmetric about the -axis. What is the maximum possible area of the rectangle?
Answer and explanation
Correct answer: A.
- Step 1: Let be the upper-right vertex with . The rectangle has width and height , giving area .
- Step 2: Differentiate with respect to to find critical points: .
- Step 3: Calculate the maximum area at : .
Answer
.
Why not the others: Other values evaluate the area of non-optimal rectangles or omit the factor of 2 representing the symmetric base width on both sides of the vertical axis.
Practise more Differentiation.
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