CUET · MATHS · PYQ PAPER 2025
The function \(f(x)=\tan x-x\):
- A is a decreasing function on \(\left[0, \frac{\pi}{2}\right)\)
- B is an increasing function on \(\left[0, \frac{\pi}{2}\right)\)
- C is a constant function
- D is neither increasing nor decreasing function on \(\left[0, \frac{\pi}{2}\right)\)
Answer & Solution
Correct Answer
(B) is an increasing function on \(\left[0, \frac{\pi}{2}\right)\)
Step-by-step Solution
Detailed explanation
\(f'(x) = \sec^2 x - 1\) \(f'(x) = \tan^2 x\) For \(x \in \left[0, \frac{\pi}{2}\right)\), \(\tan^2 x \ge 0\). \(f(x)\) is an increasing function on \(\left[0, \frac{\pi}{2}\right)\).
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