3.2E   Concavity and Point of Inflection

Concavity and Point of Inflection

    Unlike calculus, we are going to look at concavity graphically. 

    Calculus will focus on the slope of the tangent lines.

      ~  Concavity describes the shape of a graph.

      ~  When a graph opens upward, we say it is concaving up. 

               The purple region is concaving up from x = 0 to 1.75. 

                (It looks like a cup or a valley.)

      ~  When a graph opens downward, we say it is concaving down. 

               The pink area is concaving down from x = -1.75 to 0. 

                (It looks like an upside-down cup or a peak.)

      ~  The point where concavity changes is identified as the point of inflection. 

                In this case, the point of inflection occurs at (0, 0).