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

1.	Find the minimum value of the function`f(x)=(pi^2)/(16cot^(-1)(-x))-cot^(-1)x`
Answer» `f(x) = pi^2/(16cot^-1(-x)) - cot^-1x` `=>f(x) = pi^2/(16cot^-1(-x)) - (pi-cot^-1(-x))` `=>f(x) = cot^-1(-x)+pi^2/(16cot^-1(-x)) - pi` `=>f(x) = (sqrt(cot^-1(-x)) - pi/(4sqrt(cot^-1(-x))))^2+pi/2 - pi` Now, minimum value of `(sqrt(cot^-1(-x)) - pi/(4sqrt(cot^-1(-x))))^2` will be `0` as square of a number can not be less than `0`. `:. f(x)_min = pi/2 - pi = -pi/2.`

Discussion

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