Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) \[ f(x)=x^{3}+3 x^{2}-24 x \] \[ x= \]

Step 1 ：The critical numbers of a function are the x-values where the derivative of the function is either zero or undefined. So, to find the critical numbers of this function, we first need to find its derivative.

Step 2 ：Given the function \(f(x) = x^{3} + 3x^{2} - 24x\), we find its derivative \(f'(x) = 3x^{2} + 6x - 24\).

Step 3 ：Now that we have the derivative of the function, we need to find the x-values where this derivative is zero. We can do this by setting the derivative equal to zero and solving for x.

Step 4 ：Solving the equation \(3x^{2} + 6x - 24 = 0\), we find the critical numbers to be \(-4, 2\).

Step 5 ：Final Answer: The critical numbers of the function are \(\boxed{-4, 2}\).