Consider an arbitrary quadratic function q(x), given in standard form as

q(x)= ax^2 + bx + c

a) Prove that, within an interval r <_ x <_ s, the AVERAGE rate of change of q(x) is precisely a(r + s)+b [Necessarily, r does not = s in this case]

b) Deduce that, over the interval -r <_ x <_r, the AVERAGE rate of change of q(x) is just "b".

c) Use the result of part a) to deduce that the INSTANTANEOUS rate of change of q(x) at the point x = r is 2ar + b.