JEE Mains · Maths · STD 12 - 6. Application of derivatives
Let \(\quad f(x)=\left|\begin{array}{ccc}1+\sin ^2 x & \cos ^2 x & \sin 2 x \\ \sin ^2 x & 1+\cos ^2 x & \sin 2 x \\ \sin ^2 x & \cos ^2 x & 1+\sin 2 x\end{array}\right|\), \(x \in\left[\frac{\pi}{6}, \frac{\pi}{3}\right]\). If \(\alpha\) and \( \beta\) respectively are the maximum and the minimum values of \(f\), then
- A \(\beta^2-2 \sqrt{\alpha}=\frac{19}{4}\)
- B \(\beta^2+2 \sqrt{\alpha}=\frac{19}{4}\)
- C \(\alpha^2-\beta^2=4 \sqrt{3}\)
- D \(\alpha^2+\beta^2=\frac{9}{2}\)
Answer & Solution
Correct Answer
(A) \(\beta^2-2 \sqrt{\alpha}=\frac{19}{4}\)
Step-by-step Solution
Detailed explanation
\(C _1 \rightarrow C _1+ C _2+ C _3\) \(f(x)=\left|\begin{array}{ccc}2+\sin 2 x & \cos ^2 x & \sin 2 x \\ 2+\sin 2 x & 1+\cos ^2 x & \sin 2 x \\ 2+\sin 2 x & \cos ^2 x & 1+\sin 2 x\end{array}\right|\)…
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