LimitsHard
Question
Let f : R → R be a function such that f 
, f(0) = 0 and f′(0) = 3, then
, f(0) = 0 and f′(0) = 3, thenOptions
A.
is differentiable in R
is differentiable in RB.f(x) is continuous but not differentiable in R
C.f(x) is continuous in R
D.f(x) is bounded in R
Solution
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 - h) = f(x)
⇒ f(x) is continuous for all x in R
Given that f′(0) = 3
⇒
.....(1) f(0) = 0, f′(0) = 3Put x = 3x and y = 0
f(x) =
........(2)= = f(x)Similarly we can prove
f(x - h) = f(x)⇒ f(x) is continuous for all x in R
Given that f′(0) = 3
⇒
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