Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Let f : R → R be a function such that f 
= 
, f(0) = 0 and f ′ (0) = 3, then
A
is differentiable in R
B
f(x) is continuous but not differentiable in R
C
f(x) is continuous in R
D
f(x) is bounded in R
Text Solution
Verified by ExpertsThe correct answer is:
C
f 
= 
.......(1) f(0) = 0, f '(0) = 3
Put x = 3x and y = 0
f(x) = 
........(2)
= 
= 
= 
= f(x)
Similarly we can prove 
f(x) is continuous for all x in R
Given that f '(0) = 3 ⇒ 
= 
= 3
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