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JEE Mains · Maths · STD 12 - 6. Application of derivatives
The area (in sq. units) of the largest rectangle \(ABCD\) whose vertices \(A\) and \(B\) lie on the \(x\)-axis and vertices \(C\) and \(D\) lie on the parabola, \(y = x ^{2}-1\) below the \(x\) -axis, is
- A \(\frac{4}{3 \sqrt{3}}\)
- B \(\frac{1}{3 \sqrt{3}}\)
- C \(\frac{4}{3}\)
- D \(\frac{2}{3 \sqrt{3}}\)
Answer & Solution
Correct Answer
(A) \(\frac{4}{3 \sqrt{3}}\)
Step-by-step Solution
Detailed explanation
Area \(( A )=2 t \cdot\left(1- t ^{2}\right)\) \((0< t <1)\) \(A =2 t -2 t ^{3}\) \(\frac{ dA }{ dt }=2-6 t ^{2}\) \(t =\frac{1}{\sqrt{3}}\) \(\Rightarrow A_{\max }=\frac{2}{\sqrt{3}}\left(1-\frac{1}{3}\right)=\frac{4}{3 \sqrt{3}}\)
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