For the polynomial $f(x)=3 x^{3}-x^{2}-16 x-5$ determine the average rate of change between the two given values for $x$. Round to two decimal places.
\[
x=1, x=1.4
\]

Step 1 ：We are given the polynomial function \(f(x)=3 x^{3}-x^{2}-16 x-5\) and we need to find the average rate of change between \(x=1\) and \(x=1.4\).

Step 2 ：The average rate of change of a function between two points is given by the difference in the y-values of the function at those points divided by the difference in the x-values. In other words, it is the slope of the secant line passing through those two points.

Step 3 ：First, we need to calculate \(f(1.4)\) and \(f(1)\).

Step 4 ：Substituting \(x=1\) into the function, we get \(f(1) = -19\).

Step 5 ：Substituting \(x=1.4\) into the function, we get \(f(1.4) = -21.128\).

Step 6 ：Next, we find the difference between these two values and divide it by the difference in x-values, which is \(1.4 - 1 = 0.4\).

Step 7 ：The average rate of change is therefore \((-21.128 - (-19)) / 0.4 = -5.32\).

Step 8 ：Final Answer: The average rate of change of the function \(f(x)\) between \(x=1\) and \(x=1.4\) is \(\boxed{-5.32}\).