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Given A(0,0) and B(x,y) with x in(0,1) a...

Given A`(0,0)` and B`(x,y)` with `x` in`(0,1)` and `y>0` Let the slope of line AB be `m_1`. Point C lies on line `x=1` such that the slope of BC is equal to `m_2` where` 0ltm_2ltm_1`. If the area of triangle ABC can be expressed as `(m_1-m_2)f(x)` then the largest possible value of x is

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