Find the minimum value of the function `f(x) = (pi^(2))/(16 cot^(-1) (-x)) - cot^(-1) x`

Explanation

`f(x) = (pi^(2))/(16 cot^(-1) (-x)) - (pi - cot^(-1) (-x))`
`= cot^(-1) (-x) + (pi^(2))/(16 cot^(-1) (-x)) - pi`
`= (sqrt(cot^(-1) (-x)) - (pi)/(4sqrt(cot^(-1) (-x))))^(2) + (pi)/(2) - pi ge - (pi)/(2)`
`f_("min") = -(pi)/(2)`