When a function is concave up it means the average rate of change increases as the it moves from side to side. Then when it is concave down the average rate of change decreases as it moves side to side. This means that is I move the the point of intersection from left to right it would either increase or decrease but I think the secant line concavity still remains the same. https://ggbm.at/jWF9c96r this link is from the app I was using to help me with this assignment. It showed me how the solutions work for the concavity of the graph and it relevancy. The graph below is an example of the demo I used to hep me understand how the concave graphs really work. One thing I would say I don’t understand is why the graphs show up the way they do. Usually you would think up or down to be as its said but to me I get confused on which one is concave up or down. Do any of you guys have any ideas on what I can do to help me understand how to determine easily which one is up or down?

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I love the way you have explain rise over run, I haven’t thought about it previously but now that Im well inform ill start using it in my every day activities

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You did a great job explaining!

That is a tricky thing to understand how to decipher… I think the best trick is to see which direction the graph is continuously going increasing or decreasing in the y-axis. Does that make sense?

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I really like this blog post.

Also, I agree, it is sometimes confusing which one is concave up versus concave down. Here is one thing to keep in mind, a big negative number like -20 is actually less than a smaller negative number like -3. That means that if the average rate of change goes from -20 to -3 then the graph is concave up because the average rate of change is increasing! However, on the graph you see that the secant line is becoming less steep. A line with slope -20 is downward sloping and very steep. A line with slope -3 is downward sloping but very shallow. That’s backwards from what a slope of 3 to 20 (also concave up.)

The easiest thing to do is remember that there are two separate ideas:

(1) The graph can be increasing or decreasing, and

(2) the graph can be concave up or concave down.

This means there are four possibilities: concave up / increasing, concave up / decreasing, concave down / increasing, concave down / decreasing. You should try drawing each of these four possibilities.

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Thank you for the advice.

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