Let \[f(x)\] satisfy all the conditions of mean value theorem in [0, 2]. If f (0) = 0 and \[|f'(x)|\,\le \frac{1}{2}\] for all x, in [0, 2] then

\[f(x)=3\]for at least one x in [0, 2]

Let \[f(x)\] satisfy all the conditions of mean value theorem in [0, 2

1.	Let \[f(x)\] satisfy all the conditions of mean value theorem in [0, 2]. If f (0) = 0 and \[\|f'(x)\|\,\le \frac{1}{2}\] for all x, in [0, 2] then
A.	\[f(x)\le 2\]
B.	\[\|f(x)\|\le 1\]
C.	\[f(x)=2x\]
D.	\[f(x)=3\]for at least one x in [0, 2]
Answer» C. \[f(x)=2x\]

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Let \[f(x)\] satisfy all the conditions of mean value theorem in [0, 2]. If f (0) = 0 and \[|f'(x)|\,\le \frac{1}{2}\] for all x, in [0, 2] then

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