Calculus › Section D · Applications of derivatives › Topic D.2
Rolle's theorem and the mean value theorem
If you average 80 km/h on a road trip, at some instant your speedometer read exactly 80. That is not folk wisdom but a theorem, and it quietly holds up most of what comes after it in calculus.
In this topic
- Two toll booths
- Rolle's theorem
- Why Rolle's theorem is true
- Worked example: spotting the promised point
- The Mean Value Theorem
- Worked example: finding c
- The camera's argument, made precise
- Two consequences that run the course
- Why the MVT is really here
- Common mistakes to avoid
- Key takeaways
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Standards: 5