Mathematics

To find absolute extrema on a closed interval, you need to check three places: where the derivative equals zero (critical points), where the derivative doesn't exist, and the endpoints. Start by finding $h'(x)$ and solving $h'(x)=0$ to locate critical points, then evaluate $h(x)$ at each critical point and both endpoints. The largest value is your absolute maximum, and the smallest is your absolute minimum—don't assume critical points are extrema without comparing all candidates.

To find absolute extrema on a closed interval, you need to check three places: where the derivative equals zero (critical points), where the derivative doesn't exist, and the endpoints. Start by finding $h'(x)$ and solving $h'(x)=0$ to locate critical points, then evaluate $h(x)$ at each critical point and both endpoints. The largest value is your absolute maximum, and the smallest is your absolute minimum—don't assume critical points are extrema without comparing all candidates.