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

Suppose f(x) is a function satisfying the folowing conditions:
(i)f(0)=2,f(1)=1
(ii) f(x) 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)+f(3) is

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The correct Answer is:
`a=1/4, b=-5/4`
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