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GUJCET · Maths · Application of Derivatives
The function \(f(x)=\tan x-4 x\) is strictly decreasing on ___________ .
- A \(\left(-\frac{\pi}{2}, \frac{\pi}{3}\right)\)
- B \(\left(-\frac{\pi}{3}, \pi\right)\)
- C \(\left(-\frac{\pi}{3}, \frac{\pi}{3}\right)\)
- D \(\left(-\frac{\pi}{3}, \frac{\pi}{2}\right)\)
Answer & Solution
Correct Answer
(C) \(\left(-\frac{\pi}{3}, \frac{\pi}{3}\right)\)
Step-by-step Solution
Detailed explanation
\(f'(x) = \sec^2 x - 4\) \(f'(x) < 0 \implies \sec^2 x - 4 < 0\)
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