Suppose, f(x) is a functibn satisfuing the following conditions :
(a) f(0) = 2, f(1) = 1
(b) f has a minimum value at x = 5/2, and
(c) for all x,
f'(x) = |(2ax, 2ax - 1, 2ax + b + 1), (b, b + 1, - 1), (2(ax + b), 2ax + 2b + 1, 2ax + b)|
where a, b are some constants. Determine the constants a, b and the function f(x).
