QJEEM24Mad393: JEE Main 2024 Mathematics - Class 12 JEEM24Mad393 Solution: Let A be the region enclosed by the parabola y 2 = 2 x and the…

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QJEEM24Mad393: JEE Main 2024 Mathematics - Class 12 JEEM24Mad393 Solution: Let A be the region enclosed by the parabola y 2 = 2 x and the…

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 inscribed in the region $A$ is ________.

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Accepted Answer

$\begin{aligned} y^{2} = 2 x \\ a = (\frac{1}{2}) \end{aligned}$

JEE Main 2024 (Online) 8th April Evening Shift Mathematics - Application of Derivatives Question 15 English Explanation 1

$\begin{aligned} A (t) = 2 t \times (24 - \frac{t^{2}}{2}) \\ A = 48 t - t^{3} \end{aligned}$

JEE Main 2024 (Online) 8th April Evening Shift Mathematics - Application of Derivatives Question 15 English Explanation 2

$\begin{aligned} \frac{d A}{d t} = 48 - 3 t^{2} \\ 48 - 3 t^{2} = 0 \\ 3 t^{2} = 48 \\ t^{2} = 16 \\ t = \pm 4 \end{aligned}$

JEE Main 2024 (Online) 8th April Evening Shift Mathematics - Application of Derivatives Question 15 English Explanation 3

$\begin{aligned} A (4) = 48 \times 4 - 4^{3} \\ = 192 - 64 \\ A (4) = 128 \end{aligned}$

QJEEM24Mad393: JEE Main 2024 Mathematics - Class 12 JEEM24Mad393 Solution: Let A be the region enclosed by the parabola y 2 = 2 x and the…

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