Applications of Derivatives
Optimization — Inscribed Rectangle in Parabola
nta_pyq_2024_apr
Grade 12
Question:
Let $A$ be the region enclosed by the parabola $y^2=2x$ and the line $x=24$. Then the maximum area of the rectangle inscribed in the region $A$ is ________.
Step-by-Step Solution
Key Concept: Area $=2b(24-b^2/2)$. $dA/db=0\Rightarrow b=4$. Max area $=128$.
Max area $=2\cdot4\cdot16=128$.
Correct Answer: 128