Key Takeaways
Lesson Description
Key Takeaways
• Critical points occur where f'(x)=0 or where the derivative is undefined.
• The First Derivative Test determines increasing/decreasing intervals and local extrema.
• The Second Derivative Test determines concavity and classifies critical points.
• Inflection points occur where concavity changes.
• Curve sketching combines limits, derivatives, and concavity.
Must Know Equations
Critical Point:
f'(x)=0
Second Derivative:
f''(x)
Must Know Vocabulary
Critical Point
Local Maximum
Local Minimum
Increasing
Decreasing
Concavity
Inflection Point
AP Exam Focus
• Determine intervals of increase and decrease.
• Identify local extrema.
• Analyze concavity and inflection points.
• Sketch graphs using derivative information.