Academic Standard: Cluster
Use first and second derivatives to analyze a function.
Tennessee State Standards
No grade range
Relate the increasing and decreasing behavior of f to the sign of f' both analytically and graphically.
Use the first derivative to find extrema (local and global).
Analytically locate the intervals on which a function is increasing, decreasing, or neither.
Relate the concavity of f to the sign of f both analytically and graphically.
Use the second derivative to find points of inflection as points where concavity changes.
Analytically locate intervals on which a function is concave up, concave down, or neither.
Relate corresponding characteristics of the graphs of f, f', and f.
Translate verbal descriptions into equations involving derivatives and vice versa.