In the Mean-Value theorem \[\frac{f(b)-f(a)}{b-a}=f'(c),\] if \[a=0,b=\frac{1}{2}\] and \[f(x)=x(x-1)(x-2),\]the value of c is [MP PET 2003]

In the Mean-Value theorem \[\frac{f(b)-f(a)}{b-a}=f'(c),\] if \[a=0,b=

1.	In the Mean-Value theorem \[\frac{f(b)-f(a)}{b-a}=f'(c),\] if \[a=0,b=\frac{1}{2}\] and \[f(x)=x(x-1)(x-2),\]the value of c is [MP PET 2003]
A.	\[1-\frac{\sqrt{15}}{6}\]
B.	\[1+\sqrt{15}\]
C.	\[1-\frac{\sqrt{21}}{6}\]
D.	\[1+\sqrt{21}\]
Answer» D. \[1+\sqrt{21}\]

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In the Mean-Value theorem \[\frac{f(b)-f(a)}{b-a}=f'(c),\] if \[a=0,b=\frac{1}{2}\] and \[f(x)=x(x-1)(x-2),\]the value of c is [MP PET 2003]

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