The First Derivative Test
Reference: Stewart 3.3 • Chapter: 3 • Section: 3
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Chapter 3.3: What Derivatives Tell Us about the Shape of a Graph | Course: MATH161 | Difficulty: Intermediate | Time: ~25 min
Overview
This skill covers the following topics from Stewart Calculus Stewart 3.3:
- Sign change at critical point
- Local max vs min
- No sign change
Why This Matters
Understanding the first derivative test is essential for mastering what derivatives tell us about the shape of a graph.
Prerequisites
Before learning this skill, you should be comfortable with:
Key Concepts
Concept 1
Concept 2
Worked Examples
Example 1
Example 2
Common Mistakes
Practice Problems
Guided Practice
Independent Practice
Self-Assessment
Check Your Understanding
- Can you explain the main concept in your own words?
- Can you work through the examples without looking at the solution?
- Can you identify when to use this technique?
What's Next?
After mastering this skill, you'll be ready for: