Geometric View

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We present the visual interpretation of concavity and how it is determined by the second derivative.

Video Lecture

Text and Additional Details

As we move forward into discussing the meaning of higher derivatives, we start with a geometric look at one of the key interpretations of the second derivative: concavity. Since this is a visual interpretation, it is best demonstrated via the video above. From this we can conclude that concavity at a point can intuitively be thought of as a force pulling steadily on the graph, with the point as the anchor keeping the graph from moving.