Calculus Derivatives and Curve Sketching

Vocabulary flashcards covering the applications of first and second derivatives, including concavity, inflection points, and derivative tests.

First derivative

Used to determine the intervals where the function $f$ is increasing or decreasing (Inc/Dec).

First derivative test

A test for extrema that analyzes when the first derivative changes signs.

Second derivative

Determines whether the function $f$ is concave up (CU) or concave down (CD).

Inflection Point (IP)

A point where concavity changes, occurring where the second derivative $f''$ changes signs.

Second derivative test

A test that uses the second derivative to determine whether a critical point corresponds to a local minimum or maximum (min/max).