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
Create a free account to view solution
View Solution FreeMore Continuity and Differentiability Questions
If f(x) = , then f(x) is -...Let [x] denote the greatest integer less than or equal to x. If f(x) = [x sin πx], then f(x) is...If f(x) = | x - a | + | x + b |, x ∈ R, b > a > 0. Then -...Let f(x) be a polynomial of degree two which is positive for all x ∈ R If g(x) = f(x) + f′(x) + f″(x) ...Which one of the following statements is not correct ?...