Choose the minimum value of `(2x^(2) + 12x - 3)/(1 + 18x -3x^(2))` from the following options :
(a) `(-15)/(29)`, (b) `15/28` , (c ) `(-15)/(28)`, (d) None of these

Explanation

For the minimum value of `(2x^(2)- 12x + 3)/(1+18x+3x^(2)), 2x^(2) - 12x + 3` is minimum and `1+18x-3x^(2)` is maximum.
The minimum value of `2x^(2) -12x +3` occurs at `x = (-b)/(2a) = (-(-12))/(2xx2) = 3`.
The maximum value of `1+18x-3x^(2)` occurs at `x = (-b)/(2a) = (-18)/(2xx-3) = 3`.
Minimum value of given expresson is `(2(3)^(2) - 12(3) + 3)/(1+18(3) - 3(3)^(2)) = (18-36+3)/(55-27) = (-15)/(28)`.