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