Let f be a continuous function defined on the closed interval [a,b]. Answer the following questions.
a. (i) State the definition of the average value of a continuous function on a closed interval.
b. (ii) If the average value of f on [a,b] is a constant k, show that ∫abf(x)dx=k(b−a).
c. (iii) The function g(x)=3x2 is continuous on [2,h] and its average value on this interval is 30. Write, in terms of h, the equation that must be satisfied by h. (You need not solve the equation.)