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

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

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

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