Question

$f\left(x\right)=cos\left(\frac{\pi }{x}\right),x\ne 0$ increases in the interval

• A. $(\frac{1}{2k+1},\frac{1}{2k})$
• B. $(\frac{1}{2k}+2,\frac{1}{2k}+1)$
• C. $(\frac{1}{2k}+1,\frac{1}{2k}+3)$
• D. $(\frac{1}{2k+1},\frac{1}{2k}+3)$

Answer 1

The correct option is A $(\frac{1}{2k+1},\frac{1}{2k})$

f(x) = cos $\left(\frac{\pi }{x}\right)$
Thus
f(x) = cos $\left(\frac{\pi }{x}\right)$
increases in
$\frac{1}{3}\to \frac{1}{2}$
generalizing it
$(\frac{1}{2k+1},\frac{1}{2k})$