WBJEE · Maths · Application of Derivatives
Let \(f(x)=\cos \left(\frac{\pi}{x}\right), x \neq 0,\) then assuming \(k\) as an integer,
- A \(f(x)\) increases in the interval \(\left(\frac{1}{2 k+1}, \frac{1}{2 k}\right)\)
- B \(f(x)\) decreases in the interval \(\left(\frac{1}{2 k+1}, \frac{1}{2 k}\right)\)
- C \(f(x)\) decreases in the interval \(\left(\frac{1}{2 k+2}, \frac{1}{2 k+1}\right)\)
- D \(f(x)\) increases in the interval \(\left(\frac{1}{2 k+2}, \frac{1}{2 k+1}\right)\)
Answer & Solution
Correct Answer
(C) \(f(x)\) decreases in the interval \(\left(\frac{1}{2 k+2}, \frac{1}{2 k+1}\right)\)
Step-by-step Solution
Detailed explanation
\(f(x)=\cos \left(\frac{\pi}{x}\right)\) \(\Rightarrow \quad f'(x)=-\sin \left(\frac{\pi}{x}\right)\left(\frac{-\pi}{x^{2}}\right)=\frac{\pi}{x^{2}} \sin \frac{\pi}{x}\) For increasing function, \(f'(x)>0\)…
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