JEE MATHEMATICS MCQ: DIFFERENTIATION

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Analyzing +4 | -1

Let

f\left( {x + y} \right) = f\left( x \right) + f\left( y \right)

and

f\left( x \right) = {x^2}g\left( x \right)

for all

x,y \in R

, where

g\left( x \right)

is continuous function. Then,

f'\left( x \right)

is equal to

View answer and explanation

Correct option: D

Option D (0) is correct because, given f(x+y) = f(x) + f(y) and f(x) = x²g(x), it implies f(x) = 0 for all x, thus f'(x) = 0.

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