JEE Mains · Maths · STD 12 - 6. Application of derivatives
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 \(\mathrm{A}\) is ...........
- A \(128\)
- B \(129\)
- C \(130\)
- D \(178\)
Answer & Solution
Correct Answer
(A) \(128\)
Step-by-step Solution
Detailed explanation
\( \mathrm{A}=2\left(24-\frac{\mathrm{b}^2}{2}\right) \cdot \mathrm{b} \) \( \frac{\mathrm{dA}}{\mathrm{db}}=0 \quad \Rightarrow \quad \mathrm{b}=4 \) \( \mathrm{~A}=2(24-8) 4 \) \( =128\)
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