A function fff is defined such that f(x+y)=f(x)f(y)f(x+y) = f(x)f(y)f(x+y)=f(x)f(y) for all x,yx, yx,y. If f(0)≠0f(0) \neq 0f(0)=0 and f′(0)=kf'(0) = kf′(0)=k, show that f′(x)=kf(x)f'(x) = k f(x)f′(x)=kf(x).
True by limit definition of derivative
True only if f(x) is a polynomial
False
True only for x=0x=0x=0