LimitsHard
Question
Suppose that f is a differentiable function with the property that f(x + y) = f(x) + f(y) + xy and 
f(h) = 3, then
f(h) = 3, then Options
A.f is a linear function
B.f(x) = 3x + x2
C.f(x) = 3x + x2/2
D.none of these
Solution
Given f(x + y) = f(x) + f(y) + xy ........(1)
and
= 3
f′(x) =
= 3 + x
⇒ f(x) = 3x +
+ c
in equation (1) put x = 0 = y ⇒ f(0) = 0
Therefor f(x) = 3x +
and
= 3f′(x) =
= 3 + x⇒ f(x) = 3x +
+ cin equation (1) put x = 0 = y ⇒ f(0) = 0
Therefor f(x) = 3x +
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