If $f(x-y), f(x) f(y)$ and $f(x+y)$ are in A.P. for all $x, y \in R$ and $f(0)=0$, then

$f^{\prime}(-3)+f^{\prime}(3)=0$

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

1 of 1

Analyzing +4 | -1

f(x-y), f(x) f(y)

and

f(x+y)

are in A.P. for all

x, y \in R

and

f(0)=0

, then

View answer and explanation

Correct option: A

f^{\prime}(-2)=f^{\prime}(2)

Option A (

f^{\prime}(-2)=f^{\prime}(2)

) is correct because the given condition implies that f(x) is an odd function, which means its derivative f'(x) is an even function.

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