JEE Main 2024 Mathematics question
Let A be the region enclosed by the parabola y² = 2x and the line x = 24. Then the maximum area of the rectangle inscribed in the region A is .
Answer: 128
Solution
A rectangle symmetric about the x-axis with a vertex at (x, √(2x)) has area 2√(2x)(24 − x). Maximising: x = 8, area = 2 × 4 × 16 = 128.