If The Function , (where [.] Denotes The Greatest Integer Function) Is Continuous And Differentiable In (4, 6), Then.

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Question

If the function , (where [.] denotes the greatest integer function) is continuous and differentiable in (4, 6), then.

Solution

Correct option is

a Ïµ [64, ∞)

We have, x Ïµ (4, 6) 

⇒      2 < x – 2 < 4  

For f (x) to be continuous and differentiable in  must attain a constant value for x Ïµ (4, 6) 

Clearly, this is possible only when a ≥ 64 

In that case, we have 

f (x) = a cos (x – 2) which is continuous and differentiable

          a Ïµ [64, ∞)

Testing

SIMILAR QUESTIONS

Q1

The left hand derivative of f (x) = [x] sin (πx) at x = kk is an integer, is:

Q2

Which of the following functions is differentiable at x = 0?

Q3

Let f (x) = [n + p sin x], x Ïµ (0, π), n Ïµ Z and p is a prime number, where [.] denotes the greatest integer function. Then find the number of points where f (x) is not Differential.

Q4

, then draw the graph of f (x) in the interval [–2, 2] and discuss the continuity and differentiability in [–2, 2]

Q5

Fill in the blank, statement given below let . The set of points where f (x) is twice differentiable is ……………. .

Q6

The function f (x) = (x2 – 1) |x2 – 3x +2| + cos ( | | ) is not differentiable at

Q7
Q8

The number of points in (1, 3), where is not differentiable is:

Q9

Let f and g be differentiable function satisfying g’ (a) = 2, g (a) = b and fog = I (identity function) Then, f’(b) is equal to:

Q10

Let [.] denotes the greatest integer function and f (x) = [tan2x], then: