Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Let f : R → R be a function satisfying
f(x + y) = f(x) + λ xy + 3x 2 y 2 for all x, y ∈ R. If f(3) = 4 and f(5) = 52 then f ' (x) is equal to -
Text Solution
Verified by ExpertsThe correct answer is:
B
Put x = x, y = h
f(x + h) – f(x) = λ xh + 3x 2 h 2 
= λ x
⇒ f '(x) = λ x
x = 3, y = 2
f(5) = f(3) + λ (6) + 3(3)
2 (2) 2 48 = 6 λ + 108 ⇒ λ = – 10
f '(x) = – 10x
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