AP EAMCET · Maths · Application of Derivatives
The ordinates of the points on the curve \(y=\tan ^{-1}\) \((\sin \sqrt{x}), 0 \leq x \leq 8 \pi^2\), at which the tangent is parallel to \(\mathrm{x}\)-axis are
- A \(\pm \frac{\pi}{3}\)
- B \(\pm \frac{\pi}{6}\)
- C \(\pm \frac{\pi}{4}\)
- D \(\pm \frac{\pi}{2}\)
Answer & Solution
Correct Answer
(C) \(\pm \frac{\pi}{4}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text {} y=\tan ^{-1}(\sin \sqrt{x}) \\ & \Rightarrow \tan y=\sin \sqrt{x} \Rightarrow \sec ^2 y \cdot \frac{d y}{d x}=\frac{1}{\sqrt{x}} \cdot \frac{1}{2} \cos \sqrt{x} \\ & \Rightarrow \frac{d y}{d x}=\frac{\cos \sqrt{x}}{2 \sqrt{x} \sec ^2 y} \end{aligned}…
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