Given the function f(x) defined as:
[tex]f(x)=4x³[/tex]The average value on the interval [1, 4] is given by:
[tex]\bar{f}=\frac{f(4)-f(1)}{4-1}[/tex]Evaluating the function at x = 4 and x = 1:
[tex]\begin{gathered} f(4)=4\cdot4³=256 \\ \\ f(1)=4\cdot1³=4 \end{gathered}[/tex]Using these values for the average value of f:
[tex]\begin{gathered} \bar{f}=\frac{256-4}{3}=\frac{252}{3} \\ \\ \therefore\bar{f}=84 \end{gathered}[/tex]