Mathematics

To find an absolute minimum on a closed interval, you need to check three types of locations: critical points (where $p'(x) = 0$), points where the derivative doesn't exist, and the endpoints. The key insight is that the absolute minimum must occur at one of these candidates—so evaluate $p(x)$ at each and compare. Start by finding where $p'(x) = 0$, then systematically test all candidates to identify which gives the smallest value.

To find an absolute minimum on a closed interval, you need to check three types of locations: critical points (where $p'(x) = 0$), points where the derivative doesn't exist, and the endpoints. The key insight is that the absolute minimum must occur at one of these candidates—so evaluate $p(x)$ at each and compare. Start by finding where $p'(x) = 0$, then systematically test all candidates to identify which gives the smallest value.