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

1) f(1)=5

2) f(3)=21

3)for all real values of a and b, f(a+b)-f(a)=kab+2b^2

a)use a=1 and b=2 to find the value of k

f(1+2)-f(1)=k(1)(2)+2(2)^2

f(3)-f(1)=2k+8

21-5=2k+8

8=2k

k=4

Is that right?

B)find f'(3)

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

I need help figuring out how to do the other 2 parts.