Calculus-Master
Start Free Trial

Interpreting the Graph of f'

Using the graph of the derivative to determine features of the original function $f(x)$.

Core Theorem
First Derivative Test: ff has a relative max where f′f' changes from positive to negative. Concavity: ff is concave up where f′f' is increasing (f′′>0f'' > 0).

Practice Exercises

Example 01Easy
Given the graph of f′f', if f′f' crosses from above the x-axis to below at x=3x=3, what happens to ff at x=3x=3?
NEED A HINT?
Check the sign change of f′f'.
SHOW DETAILED EXPLANATION

Conclusion

f(x)f(x) has a relative maximum at x=3x=3 because f′f' changes from positive to negative.
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 →

Free Access Up to Day 7 · No Credit Card Required