A function f is defined for all real numbers and has the following properties.

(i) f(1)=5

(ii) f(3)=21

(iii) for all real values of a and b, f(a+b) - f(a)= kab+2b^2 where k is a fixed real number independent of a and b

a) Use a=1 and b=2 to find k.

b) Find f'(3)

c) Find f'(x) and f(x) for all real x

So I found out that k=-4, but I'm stuck on how to find the original equation and thus the derivative by the given info.