Calculus › Section D · Applications of derivatives › Topic D.3
Increasing, decreasing, and the first derivative test
The sign of the derivative is the mood of the graph: positive slopes mean climbing, negative mean falling. Read the sign changes and you can find every peak and valley a function has.
In this topic
- Slopes are the story
- The increasing-decreasing test
- Where the sign can change
- Worked example: mapping a cubic's moods
- The first derivative test
- Worked example: classify the turning points
- When the derivative does not exist
- Turning points in the wild
- Common mistakes to avoid
- Key takeaways
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Standards: 5