Consider the polynomials p(x)=x3−3x2+2 and q(x)=2x2−4x+1 defined on the interval [0,3].
(a) Find the average value of p on [0,3].
(b) Find the average value of q on [0,3].
(c) State which function has the larger average value on this interval.
(d) Calculate, correct to the nearest integer, the percentage by which the larger average value exceeds the smaller one.