Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Let 
satisfy f(x + y) = 2 x f(y) + 4 y f(x), 
x, 
. If f(2) = 3, then 14. 
is equal to_____.
Text Solution
Verified by ExpertsThe correct answer is:
248
(248)
Put y = 2
f(x + y) = 2 x .f(y) + 4 y .f(x).
f(x + 2) = 2 x .3+16f(x)
f ’ (x + 2) = 16f ’ (x) + 3.2 x ln2
f ’ (4) = 16f (2) + 12ln2 ....(i)
f(y + 2) = 4f(y) + 34 y
f ’ (4) = 4f ’ (y) + 3.4 y ln4
f ’ (4) = 4f ’ (2) + 961n2 ....(ii)
solving eq. (i) and (ii), we get
f ’ (2) = 7 In2
from equation (i), we get
f ’ (4)= 1241n2
Now 
=248
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