When a graph is concave up it means that the average rate of change is increasing if you move from left to right and when the graph is concave down it means that the average rate of change is decreasing as you move from left to right. For a graph to concave up, it means that the slope is increasing which means the second derivative over an interval must be greater than zero and for it to concave down it means that the slope is decreasing and the second derivative is negative. What else do you know about concavity?

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Tags: Average rate of change, Concave down, Concave up, Graphs, Math, week2-C

i love your explanation of graph that bend. you paint a good picture of how its needs to be illustrated

When you say that the ” second derivative over an interval must be greater than zero,” what do you mean by the “second derivative”?