# Mark the Correct Alternative in of the Following: Let F(X) = X − [X], X ∈ R, Then F ′ ( 1 2 ) - Mathematics

MCQ

Mark the correct alternative in of the following:

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

#### Options

•  $\frac{3}{2}$

• 1

•  −1

#### Solution

Given: f(x) = x − [x], x ∈ R
Now,
For 0 ≤ x < 1, [x] = 0.
∴ f(x) = − 0 = x, ∀ x ∈ [0, 1)
Differentiating both sides with respect to x, we get
'(x) = 1, ∀ x ∈ [0, 1)

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

Hence, the correct answer is option (b).

Concept: The Concept of Derivative - Algebra of Derivative of Functions
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 30 Derivatives
Q 1 | Page 47