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

Given A(0, 0) and B(x, y) with `x in (0, 1)` and `y gt 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 lt m_2 lt m_1`. If the area the triangle ABC can be expressed as `(m_1 - m_2) f(x)`, then find the largest possible value of f(x).

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`1/8`
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