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Given A (0, 0) and B (x,y)with x epsilon...

Given `A (0, 0)` and `B (x,y)`with `x epsilon (0,1)` and `y>0`. Let the slope of the line AB equals `m_1` Point C lies on the line `x= 1` such that the slope of BC equals `m_2` where `0< m_2< m_1` If the area of the triangle ABC can expressed as `(m_1- m_2)f(x)`, then largest possible value of `f(x)` is:

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