Let f is a differentiable function such that
None of these
Differentiating both sides we get;
f (x) + f’(x) = x2 + 2x + f (x)
Integrating (iii) both sides;
But f (0) = 0 ⇒ c = 0
Let f be an even function and f ’(0) exists, then find f’(0).
Let f (x) = xn, n 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, a, b > 0
Find the set of points where x2 |x| is true thrice differentiable.
Find the number of points where f (x) = [sin x + cos x] (where [.] denotes greatest integral function), x Ïµ [0, 2π] is not continuous.
differentiable function in [0, 2], find a and b. (where [.] denotes the greatest integer function).
Discuss the continuity of the function .
Let f : R → R, such that f’ (0) = 1 and f (x +2y) = f (x) + f (2y) + ex+2y (x + 2y) – x. ex – 2y. e2y + 4xy, ∀ x, y Ïµ R. Find f (x).
If g(x) is continuous function in [0, ∞) satisfying g(1) = 1. If
Let f : R+ → R satisfies the functional equation
If f’(1) = e, determine f (x).