Ghukasyan, Gohar. “Calculus: The First Derivative Test”. 2022. Medium. https://medium.com/@Gohar_Ghukasyan/calculus-the-first-derivative-test-9898613ceaf5.
In a nutshell, the first derivative test enables us to find increasing and decreasing intervals, critical numbers, and relative extrema.
Ghukasyan, Gohar. “Calculus: The Second Derivative Test”. 2022. Medium. https://medium.com/@Gohar_Ghukasyan/calculus-the-second-derivative-test-31bfa8b1b7a9.
Concavity describes the rate of change of a function’s derivative. If f’ is increasing then the graph is concave up, and if f’ is decreasing, then the graph is concave down. To test for concavity, we have to find the second derivative and determine whether it is positive or negative.