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Let \(f(x) =\frac{x}{-2x^2 + 5x - 2}\), for \(-2 \leq x \leq 4\), \(x \ne \frac{1}{2}\), \(x\ne2\), as shown below.

The curve has a local minimum at \(A(1;1)\) and a local maximum at \(B\).

1. Use the quotient rule to show that \(f^\prime(x)=\frac{2x^2 - 2}{(-2x^2+5x-2)^2}\).
2. Hence find the coordinates of \(B\).
3. Given that the line \(y=k\) does not meet the curve of \(f\), find the possible values of \(k\).