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

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Given \( A(0,0) \) and \( B(x, y) \) with \( x \in(0,1) \) and \( y0 \). Let the siope of line \( A B \) be \( m_{1} \). Point \( C \) lies on line \( x=1 \) such that the slope of \( B C \) is equal to \( m_{2} \), where \( 0m_{2}m_{1} \).
W If the area of triangle \( A B C \) can be expressed as \( \left(m_{1}-m_{2}\right) f(x) \) and the largest possible value of \( f(x) \) is \( \lambda \), then the value of \( \frac{1}{\lambda} \) is
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