Find the intervals of decrease and increase for the function `f(x)=cos(pi/x)`

Explanation

`f(x)=-cos(pi)/(x)` .The function is defined forall x, where `xne0`
`f(x) =-sin(pi)/(x)pi-(1)/(x^(2))=(pi)/(x^(2))sin(pi)/(x)`
Therefore f is differentiable `forall x, (xne0)`
Here sign f(x) is same as that of `sin(pi)/(x)`
Thus f(x) is positive if `sin(pi)/(x)gt0` and f(x) is negative if `sin(pi)/(x)lt0`
or `sin(pi)/(x)gt0 if 2 kpilt(pi)/(x)lt(2x+1)pi,kinz`
and `sin(pi)/(x) lt0, if (2k+1)pilt(pi)/(x)lt(2k+2)pi,kinZ`
Hence the function f is increasing in the interval `(1)/(2k+1),(1)/(2k)` and decreasing in the interval `(1)/(2k+2),(1)/(2k+1)` (k being a non negative integer).