Find the average rate of change of $f(x)=-2 x^{3}+4 x^{2}$ from $x=1$ to $x=3$ Simplify your answer as much as possible.

Step 1 ：Given the function \(f(x)=-2 x^{3}+4 x^{2}\), we are asked to find the average rate of change from \(x=1\) to \(x=3\).

Step 2 ：The average rate of change of a function \(f(x)\) from \(x=a\) to \(x=b\) is given by the formula \(\frac{f(b)-f(a)}{b-a}\).

Step 3 ：Substitute \(x=1\) and \(x=3\) into the function \(f(x)=-2 x^{3}+4 x^{2}\) to get \(f(1)\) and \(f(3)\).

Step 4 ：Substitute \(f(1)\), \(f(3)\), \(a=1\), and \(b=3\) into the formula \(\frac{f(b)-f(a)}{b-a}\) to get the average rate of change.

Step 5 ：The average rate of change of the function \(f(x)=-2 x^{3}+4 x^{2}\) from \(x=1\) to \(x=3\) is -10.0.

Step 6 ：Final Answer: \(\boxed{-10.0}\)