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Suppose f(x) is a function satisfying...

Suppose f(x) is a function satisfying the following conditions :
(i) f(0)=2,f(1)=1
(ii) f has a minimum value at `x=5//2`
(iii) for all `x,f' (x) = |{:(2ax,,2ax-1,,2ax+b+1),(b,,b+1,,-1),(2(ax+b),,2ax+2b+1,,2ax+b):}|`
The value of f(2) is

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