Order the steps of finding the global maximum of a continuous function on a closed interval.

1. Differentiate the function
2. Solve f' (x) = 0 and note where f' is undefined, giving the critical points
3. Evaluate f at every critical point lying inside the interval
4. Evaluate f at both endpoints of the interval
5. Take the largest of all the values collected

The Extreme Value Theorem guarantees the maximum exists, and it must occur at a critical point or an endpoint, so this finite list of candidates is exhaustive. Stopping after step 2 finds locations without values; skipping step 4 can miss the answer entirely.