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JEE Main 20248 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
8 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Application of Derivatives

JEE Main 2024 · 8 April · Evening Shift · Mathematics · Application of Derivatives

Let A be the region enclosed by the parabola y^2=2 x and the line...

Let A\mathrm{A} be the region enclosed by the parabola y2=2xy^2=2 x and the line x=24x=24. Then the maximum area of the rectangle inscribed in the region A\mathrm{A} is________Let A be the region enclosed by the parabola y^2=2 x and the line x=24 . Then the maximum area of the rectangle

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Step-by-step solution

Let A be the region enclosed by the parabola y^2=2 x and the line x=24 . Then the maximum area of the rectangle
A=2(24−b22)⋅bdAdb=0⇒b=4A=2(24−8)4=128\begin{aligned} & A=2\left(24-\frac{b^2}{2}\right) \cdot b \\ & \frac{d A}{d b}=0 \quad \Rightarrow \quad b=4 \\ & A=2(24-8) 4 \\ & =128\end{aligned}
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