First slide
Derivatives
Question

If function f satisfies the relation fx×f'-x=f-x×f'x for all x, and f(0) = 3, and if  f(3) =3, then the value of f(-3) is ____

Moderate
Solution

fx.f'-x=f-x.f'xorf'x×f-x-fx×f'-x=0orddxfxf-x=0orfxf-x=kGivenf02=k=9ork=9Thenf3f-3=9orf-3=3

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