Question

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

                          .

Solution

Correct option is

Here,

         

the given equation could be written as; 

         

Differentiating both sides w.r.t ‘x’, we get  

         

using (i); 

          

    

          

Which is continuous in [0, ∞)

SIMILAR QUESTIONS

Q1

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).

Q2

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

Q3

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

Q4

 

Q5

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

Q6

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

Q7

  

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

Q8

Discuss the continuity of the function .

Q9

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).

Q10

Let f is a differentiable function such that 

          .