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 f(x) = |x - a| φ(x), where φ is a continuous function and φ(a) ≠ 0. Then -...If y = sin (m sin-1x), then (1 - x2) y″ -xy′ is equal to -...If x + y = 0, then equals -...If (x) = , g(x) = and h(x) = 2x - 3, then f′(h′(g′(x)) =...