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Derivative from First Principle

If fx+y = fx ...

Question

$I f f (x + y) = f (x) + f (y) + 2 x y - 6 f o r a l l x, y i n R a n d f^{'} (0) = 2 t h e n y = f (x) w i l l b e$

S t r a i g h t l i n e

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Solution

The correct option is A $S t r a i g h t l i n e$
Given,

$f (x + y) = f (x) + f (y) + 2 x y - 6$

$y = f (x) \Rightarrow y = 0$

$∴ y = f (x) = f (x) - 6$

$\Rightarrow f (x) = y + 6$

The above equation represents equation of straight line.

Suggest Corrections

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