Interpreting the Graph of f'
Using the graph of the derivative to determine features of the original function .
First Derivative Test: has a relative max where changes from positive to negative. Concavity: is concave up where is increasing ().
Practice Exercises
Example 01Easy
Given the graph of , if crosses from above the x-axis to below at , what happens to at ?
NEED A HINT?
Check the sign change of .
SHOW DETAILED EXPLANATION
Conclusion
has a relative maximum at because changes from positive to negative.
Ready to test it?
Practice Applications & Optimization multiple-choice questions, timed and fully explained.
On the AP exam
See how this shows up on the free-response section: step-by-step method, scoring tips and practice.
Past AP Exams
Real AP exam questions on this topic
Official AP Calculus AB free-response questions, each with a full step-by-step solution.
- 2026 FRQ 4 · No calculatorAnalyzing a Function from its Derivative Graph
- 2025 FRQ 4 · No calculatorAccumulation Function from a Graph
- 2024 FRQ 4 · No calculatorRegion R and Its Accumulation Function
- 2023 FRQ 4 · No calculatorAnalyzing a Function from its Derivative Graph
- 2022 FRQ 3 · No calculatorAnalyzing a Function from its Derivative Graph
- 2021 FRQ 4 · No calculatorGraph Analysis with an Accumulation Function
Gary Chang
Calculus Educator5+ Years of Calculus Teaching Experience | AP Calculus Specialist. Dedicated to helping students master calculus through step-by-step logic and clear visualizations.
Recommended Learning Path
Want a Structured Way to Score a 5 in ap calculus ab?
Don not learn in fragments. Follow our proven 30-day roadmap that connects every concept from Limits to Integrals.
Start Your 30-Day Journey →Join thousands of students mastering AP Calculus with us.