Let f(x)=ax2+bx be a quadratic polynomial.
The following information about its average values is provided:
1. The average value of f over [0,2] is 3.
2. The average value of f over [2,4] is 11.
a. (i) Translate each of the above conditions into an algebraic equation in a and b.
b. (ii) Solve the simultaneous equations obtained in part (i) to determine the values of a and b.
c. (iii) Using the constants found, calculate the average value of f over the entire interval [0,4].