Find the absolute maximum and minimum values of each function over the indicated interval, and indicate the x-values at which they occur.
\[
f(x)=9 x^{4}-4 x^{3},[-3,3]
\]
The absolute maximum value is at $x=$ (Use a comma to separate answers as needed.)

Step 1 ：Find the derivative of the function \(f(x)=9x^4-4x^3\).

Step 2 ：Set the derivative equal to zero and solve for x to find the critical points.

Step 3 ：The critical points are \(x=0\) and \(x=1/3\).

Step 4 ：Evaluate the function at these critical points and at the endpoints of the interval, which are -3 and 3.

Step 5 ：The values at these points are 0, -1/27, 837, and 621.

Step 6 ：The highest value among these is 837, which is the absolute maximum value of the function over the interval.

Step 7 ：This maximum value occurs at \(x=-3\).

Step 8 ：Final Answer: The absolute maximum value of the function \(f(x)=9x^4-4x^3\) over the interval \([-3,3]\) is 837, and it occurs at \(x=-3\). So, the answer is \(\boxed{-3}\).