Advertisement Remove all ads

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

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads
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

Advertisement Remove all ads

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
  Is there an error in this question or solution?

APPEARS IN

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

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×