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

Suppose `f(x)` is a function satisfying the following conditions: `f(0)=2,f(1)=1` `f` has a minimum value at `x=5/2` For all `x ,f^(prime)(x)=|2a x2a x-1 2a x+b+1bb+1-1 2(a x+b)2a x+2b+1 2a x+b|` where `a , b` are some constants. Determine the constants `a , b` , and the function `f(x)`

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