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SIMILAR QUESTIONS

Q1

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

Q2

 

    

Q3

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

Q4

 

Find the number of points where f (x) = [sin x + cos x]  

(where [.] denotes greatest integral function), x Ïµ [0, 2π] is not continuous.

Q5

 

  

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

 

Q6

 

Let f : → R, such that f’ (0) = 1

and f (x +2y) = f (x) + f (2y) + ex+2y (x + 2y) – x. ex – 2y. e2y + 4xy

∀ xy Ïµ R. Find f (x).

Q7

 

If g(x) is continuous function in [0, ∞) satisfying g(1) = 1. If

     .

Q8

 

Let f is a differentiable function such that 

            .

Q9

 

Let f : R+ → R satisfies the functional equation  

          .  

If f’(1) = e, determine f (x).