Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Let g : R → R be a differentiable function satisfying g(x) = g(y) g(x – y) ∀ x, y ∈ R and g'(0) = a and g'(3) = b then g'(– 3) is -
A
B
C
D
None of these
Text Solution
Verified by ExpertsThe correct answer is:
A
Differentiating partially w.r.t. x
g'(x) = g(y)[g'(x – y)]
Put y = x
g'(x) = g(x) . g'(0) = a . g(x)
⇒ g(x) = ae x ( g(0) = 1)
Now g'(x) = ae x , g'(3) = ae 3
and g' (–3) = ae –3 = 
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