Laillanni M.

Graphs that bend upwards or downwards are called concave functions. A function that has a positive slope or increases, is called a “concave upwards” function which means the rate of change is increasing. On the other hand, a downward concave function is when the rate of change decreases. It has a negative slope or downward curve. The first graph concave upwards while the second graph concave downwards. What else do you know about concave functions?

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I really like the pictures you included. You have to be careful though. You state that “a downward concave function is when the rate of change decreases. It has a negative slope or downward curve.” You can have a graph with a negative slope that is concave up (or down.) The point is not whether the slope is negative; it’s whether the slope is decreasing. For example, you could have positive slope of 15 and then move a little to the right and have a positive slope of 3. Both of these are positive slopes. The graph would be upward sloping, but the slope is decreasing as you move to the right. 3 is smaller than 15 so the graph is concave down. I hope that makes sense!

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