Let f: R → R satisfy f(x + y) = 2ˣf(y) + 4^(y)f(x), x, y R. If f(2) = 3, then 14. (f'(4))/(f'(2)) is equal to _ _ _ _ _ _.

Limit, Continuity and Differentiability: JEE Main 2022 Mathematics question

JEE Main 2022 · 26 Jun, Evening shift · Q34

JEE Main 202226 Jun, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let f : R

\to

R satisfy

f(x + y) = {2^x}f(y) + {4^y}f(x)

\forall

x, y

\in

R. If f(2) = 3, then

14.\,{{f'(4)} \over {f'(2)}}

is equal to ____________.

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