Question

Suppose that f is a differentiable function with the property that

f(x + y) = f(x) + f(y) + xy and 

Solution

Correct option is

f(x) = 3x + x2/2

             

           

Hence f(x) = 3x + x2/2 + C. Putting x = y = 0 in the given equation, we have f(0) = f(0 + 0) = f(0) + f(0) + 0 ⇒ f(0) = 0. Thus C = 0 and f(x) = 3xx2/2.

SIMILAR QUESTIONS

Q1

 

 

Q3

 

 

Q6
Q8

If f’(x) is continuous at x = 0 and f’’(0) = 4, then the value of

Q9

Suppose f is differentiable at x = 1 and

Q10