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Points of Inflection

Finding the points of inflection and applying the second derivative to determine concavity.

Mapped to AP College Board # FUN-4, FUN-4.A, FUN-4.A.4, FUN-4.A.5, FUN-4.A.6

A function’s derivative can be used to understand some behaviors of the function. Justify conclusions about the behavior of a function based on the behavior of its derivatives. The graph of a function is concave up (down) on an open interval if the function’s derivative is increasing (decreasing) on that interval. The second derivative of a function provides information about the function and its graph, including intervals of upward or downward concavity. The second derivative of a function may be used to locate points of inflection for the graph of the original function.