Continuity and DifferentiabilityHard
Question
Suppose that f is a differentiable function with the property that f(x + y) = f(x) + f(y) + xy and 
f(h)/h = 3 then -
f(h)/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
f(x + y) = f(x) + f(y) + xy that is property
take the option
or
or f is linear function
so f(x + y) = f(x) + f(y) + xy
It take 3rd option that satisfy the property and also
= 3 so it
is required solution
take the option
or
or f is linear functionso f(x + y) = f(x) + f(y) + xy
It take 3rd option that satisfy the property and also
= 3 so itis required solution
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