1. The problem is to find the absolute minimum of a function on the closed interval $[0,4]$. 2. To find the absolute minimum on a closed interval, we evaluate the function at critical points inside the interval and at the endpoints. 3. First, find the derivative of the function and solve for critical points where the derivative is zero or undefined. 4. Next, evaluate the function at each critical point within $[0,4]$ and at the endpoints $x=0$ and $x=4$. 5. Compare these values; the smallest value is the absolute minimum on the interval. 6. This method ensures we consider all possible points where the minimum could occur, including boundaries.