Q63 / 125 · BITSAT 2017 · Mathematics

Consider the greatest integer function, defined by $f (x) = [x], 0 \leq x < 2$ . Then

Solution

The given function is

$f (x) = \{\begin{cases} 0, & 0 \leq x < 1 \\ 1, & 1 \leq x < 2 \end{cases}$

Now, $LHD = \lim_{x \to 1^{-}} \frac{f (x) - f (1)}{x - 1} = \lim_{x \to 1^{-}} \frac{0 - 1}{x - 1}$

Which does not exist

$∴ f$ is not derivable at $x = 1$ .

Hence, the correct answer is option: 'B'.