Find the average rate of change of the function on the interval specified. \[ g(x)=2 x^{3}-3 \text { on }[-3,3] \]

Step 1 ：We are given the function \(g(x) = 2x^3 - 3\) and the interval \([-3, 3]\).

Step 2 ：The average rate of change of a function on an interval \([a, b]\) is given by the formula: \(\frac{f(b) - f(a)}{b - a}\).

Step 3 ：Substitute the values into the formula: \(a = -3\), \(b = 3\), \(f(a) = g(-3) = 2(-3)^3 - 3 = -57\), \(f(b) = g(3) = 2(3)^3 - 3 = 51\).

Step 4 ：Calculate the average rate of change: \(\frac{f(b) - f(a)}{b - a} = \frac{51 - (-57)}{3 - (-3)} = 18.0\).

Step 5 ：Final Answer: The average rate of change of the function on the interval specified is \(\boxed{18}\).