CUET · MATHS · PYQ PAPER 2025
Interval in which the function \(f\) given by \(f(x)=\tan x-4 x, x \in\left(0, \frac{\pi}{2}\right)\) is strictly decreasing is
- A \(0< x<\frac{\pi}{3}\)
- B \(\frac{\pi}{3}< x<\frac{\pi}{2}\)
- C \(\frac{\pi}{4}< x< \frac{\pi}{2}\)
- D \(\frac{\pi}{2}>x>0\)
Answer & Solution
Correct Answer
(A) \(0< x<\frac{\pi}{3}\)
Step-by-step Solution
Detailed explanation
\(f'(x) = \sec^2 x - 4\) \(\sec^2 x - 4 \(\sec^2 x \(|\sec x| \(|1/\cos x| \(|\cos x| > 1/2\) Since \(x \in\left(0, \frac{\pi}{2}\right)\), \(\cos x > 0\). \(\cos x > 1/2\) For \(x \in\left(0, \frac{\pi}{2}\right)\), \(\cos x > 1/2\) when \(0 < x < \frac{\pi}{3}\).
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