Question

Let f is a differentiable function such that 

          .

Solution

Correct option is

We have,

          

  

                                                           

Differentiating both sides we get;

            

                                                                [using Leibnitz-rule] 

          f (x) + f’(x) = x2 + 2x + f (x)  

Integrating (iii) both sides;  

But    f (0) = 0      ⇒      c = 0

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

 

Q4

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

Q5

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

Q6

  

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

Q7

Discuss the continuity of the function .

Q8

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).

Q9

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

                          .

Q10

Let f : R+ → R satisfies the functional equation  

          .  

If f’(1) = e, determine f (x).