Let f : R R be a function such that f(x + y) = f(x) + f(y), x, y R . If f(x) is differentiable at x = 0, then

JEE Advanced 2011 Mathematics question

Let be a function such that , . If f(x) is differentiable at , then

(A)f(x) is differentiable only in a finite interval containing zero
(B)f(x) is continuous Correct
(C)f'(x) is constant Correct
(D)f(x) is differentiable except at finitely many points

Answer: (B),(C)

Solution

Putting gives . For any x: . Since f is differentiable at 0, this limit exists for every x and equals the constant . So f is differentiable everywhere

See the full step-by-step solution

Create a free account to read the complete working, and practise questions like this in a timed test.

Create a free account

Question ID VK-025931