Calculus › Section D · Applications of derivatives › Topic D.1
Extreme values on an interval
Finding the biggest or smallest value of a function is the oldest applied question in calculus. This topic pins down where extremes can hide, and gives a four-step method that never misses them on a closed interval.
In this topic
- Why we hunt extremes
- Absolute versus local
- The guarantee: the Extreme Value Theorem
- Critical numbers and Fermat's theorem
- Warning: critical does not mean extreme
- The closed-interval method
- Worked example: hunting on a closed interval
- Worked example: a corner wins a minimum
- What can go wrong without the hypotheses
- Common mistakes to avoid
- Key takeaways
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Standards: 5