LimitsHard
Question
If a differentiable function f satisfies f 
∀ x, y ∈ R, then f(x) is equal to
∀ x, y ∈ R, then f(x) is equal toOptions
A.1/7
B.2/7
C.8/7
D.4/7
Solution
f
∀, x, y ∈ R ......(1)
differentiate w.r.t. y
replace x with 3x and y with 0
f′(x) = - 2f′(0)
put x = 0 we get f′(0) = 0
⇒ f′(x) = 0
⇒ f(x) = constant
⇒ f(x) = f(0)
in equation (1) put x = 0 = y it gives f(0) = 4/7
⇒ f(x) = 4/7
∀, x, y ∈ R ......(1)differentiate w.r.t. y
replace x with 3x and y with 0
f′(x) = - 2f′(0)
put x = 0 we get f′(0) = 0
⇒ f′(x) = 0
⇒ f(x) = constant
⇒ f(x) = f(0)
in equation (1) put x = 0 = y it gives f(0) = 4/7
⇒ f(x) = 4/7
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