If the function \[f(x)={{x}^{3}}-6a{{x}^{2}}+5x\]satisfies the conditions of Lagrange's mean value theorem for the interval [1, 2] and the tangent to the curve \[y=f(x)\]at \[x=\frac{7}{4}\]is parallel to the chord that joins the points of intersection of the curve with the ordinates \[x=1\] and \[x=2\]. Then the value of \[a\]is [MP PET 1998]

If the function \[f(x)={{x}^{3}}-6a{{x}^{2}}+5x\]satisfies the conditi

1.	If the function \[f(x)={{x}^{3}}-6a{{x}^{2}}+5x\]satisfies the conditions of Lagrange's mean value theorem for the interval [1, 2] and the tangent to the curve \[y=f(x)\]at \[x=\frac{7}{4}\]is parallel to the chord that joins the points of intersection of the curve with the ordinates \[x=1\] and \[x=2\]. Then the value of \[a\]is [MP PET 1998]
A.	\[\frac{35}{16}\]
B.	\[\frac{35}{48}\]
C.	\[\frac{7}{16}\]
D.	\[\frac{5}{16}\]
Answer» C. \[\frac{7}{16}\]

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