Question

Mark the correct alternative in each of the following:

Let f(x) = x − [x], x ∈ R, then $f\text{'}\left(\frac{1}{2}\right)$ is

(a) $\frac{3}{2}$ (b) 1 (c) 0 (d) −1

Answer 1

Given: f(x) = x − [x], x ∈ R

Now,

For 0 ≤ x < 1, [x] = 0.

∴ f(x) = x − 0 = x, ∀ x ∈ [0, 1)

Differentiating both sides with respect to x, we get

f '(x) = 1, ∀ x ∈ [0, 1)

$\therefore f\text{'}\left(\frac{1}{2}\right)=1$

Hence, the correct answer is option (b).