The equation of a curve is $$\(y=k x^{\frac{1}{2}}-4 x^{2}+2\)$$, where $$\(k\)$$ is a constant. Points $$\(A\)$$ and $$\(B\)$$ on the curve have $$\(x\)$$-coordinates 0.25 and 1 respectively. For a different value of $$\(k\)$$, the tangents to the curve at the points $$\(A\)$$ and $$\(B\)$$ meet at a point with $$\(x\)$$-coordinate 0.6 . Find this value of $$\(k\)$$. ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ .

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