Differentiable Function In [0, 2], Find a and b. (where [.] Denotes The Greatest Integer Function).

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Question

  

differentiable function in [0, 2], find a and b. (where [.] denotes the greatest integer function).

Solution

Correct option is

Here; [x]2 = 0, for all 0 ≤ x < 1  

and    [x]2 = 1, for x = 1  

  

Hence,  

                     

As f (x) is differentiable in [0, 2] ⇒ continuous and differentiable at x = 1 

   

             

again since f (x) is differentiable at x = 1  

(LHD at x = 1) = (RHD at x = 1)   

  

⇒         3= ½

or           a = 1/6                              …(ii)  

from (i) and (ii), we get  

           

Testing

SIMILAR QUESTIONS

Q1

If f (x) is differentiable function and (f (x). g(x)) is differentiable at x = a, then

Q2

        

Determine the value of ‘a’ if possible, so that the function is continuous

Q3

 for all real x and y. If f ’ (0) exists and equals to –1and f (0) = 1, find f ’(x).

Q4

Now if it is given that there exists a positive real δ, such that f (h) = h for 0 < h < δ then find f’(x) and hence f (x).

Q5

Let f  be an even function and f ’(0) exists, then find f’(0).

Q6

Let f (x) = xnn being non-negative integer. Then find the value of n for which the equality f’(a + b) = f ’(a) + f ’ (b) is valid for all, ab > 0

Q7

 

Q8

Find the set of points where x2 |x| is true thrice differentiable.

Q9

Find the number of points where f (x) = [sin x + cos x(where [.] denotes greatest integral function), x Ïµ [0, 2π] is not continuous.

Q10

Discuss the continuity of the function .