﻿ Suppose that f is a differentiable function with the property that f(x + y) = f(x) + f(y) + xy and  : Kaysons Education

Suppose That f is A Differentiable Function With The Property That F(x + y) = f(x) + f(y) + xy and

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Question

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

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

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Suppose f is differentiable at x = 1 and

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