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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).

A

1

B

`1//2`

C

`1//4`

D

`1//8`

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A
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