Let f(x)=x-[x],x , then f' (1 2 ) is: - Vidyadip

MCQ

Let $\text{f}(\text{x})=\text{x}-[\text{x}],\text{x}\in\text{R},$ then $\text{f}'\Big(\frac{1}{2}\Big)$ is:

A
$\frac{3}{2}$
✓
$1$
C
$0$
D
$-1$

✓

Answer

Correct option: B.

$1$

Given: $\text{f}(\text{x})=\text{x}-[\text{x}],\text{x}\in\text{R}$
Now,
For $0\le\text{x}<1,[\text{x}]=0$
$\therefore\text{f}(\text{x})=\text{x}-0=\text{x},\forall\text{x}\in[0,1)$
Differentiate with respect to $x,$ we get
$\text{f}'(\text{x})=1,\forall\text{x}\in[0,1)$
$\therefore\text{f}'\Big(\frac{1}{2}\Big)=1$

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