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Question
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
0
−1
Solution
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)
\[\therefore f'\left( \frac{1}{2} \right) = 1\]
Hence, the correct answer is option (b).
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