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Let \( f(x) \) is a function satisfying the following conditions
(i) \( f(0)=2, f(1)=1 \)
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(ii) \( f(x) \) has a minimum value at \( x=5 / 2 \) and
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(iii) For all \( x, f^{\prime}(x)=\left|\begin{array}{ccc}2 a x & 2 a x-1 & 2 a x+b+1 \\ b & b+1 & -1 \\ 2(a x+b) & 2 a x+2 b+1 & 2 a x+b\end{array}\right| \)
where, \( a \) and \( b \) are some constants. Determine the constants \( a, b \) and the function \( f(x) \).
\( (1998,8 \mathrm{M}) \)
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