The Average Value of a Function G on 0 F $\le$

Multiple Choice

The average value of a function g on 0 F $\le$ x $\le$ 3 is a constant $\bar{g}$ given by $\bar{g}=\frac{1}{3-0} \int_{0}^{3} g(x) d x$ .Which of the following must be true?

A) $\int_{0}^{3} \bar{g} g(x) <(\bar{g}) ^{2}$
B) $\int_{0}^{3} \bar{g} g(x) >(\bar{g}) ^{2}$
C) $\int_{0}^{3} \bar{g} g(x) =(\bar{g}) ^{2}$
D) None of the above