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Find a function whose graph has given properties

Let f(x) be a function on the interval [0,1] that is nonnegative and differentiable, and such that f(1) = 0. If for each a in the open interval (0,1) the line given by the equation x = a divides the ordinate set of f(x) into regions A and B where A denotes the leftmost region. If the areas of the two regions obey the equation

    \[ A - B = 2f(a) + 3a + b, \]

where b is a constant that does not depend on a, find f(x) and b.


Incomplete.

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