Answer:
[tex]-\frac{1}{28}[/tex]
Step-by-step explanation:
The given function is
[tex]f(x)=-\sqrt[3]{x}[/tex]
[tex]f(64)=-\sqrt[3]{64}=-4[/tex]
[tex]f(8)=-\sqrt[3]{8}=-2[/tex]
The average rate of change of this function is the slope of the secant line connecting the points (64,f(64)) and (8,f(8));
[tex]=\frac{f(64)-f(8)}{64-8}[/tex]
We substitute the functional values into this function to obtain;
[tex]=\frac{-4--2}{56}[/tex]
This simplifies to;
[tex]=\frac{-2}{56}[/tex]
[tex]=-\frac{1}{28}[/tex]
