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course Mth 173
Use the free-form tool (you can find it easily enough; names of the tools pop up on mouse-over). Check both the integral and derivative boxes. Construct a graph that is concave up. Describe the resulting derivative and integral functions.Using the freeform tool, when I created a concave up graph the integral made a concave up graph that leveled out at the top. The derivative made a spastic up and down graph that kind of resembles a concave up graph in the overall shape tha it takes.
Now see if you can construct a graph whose derivative is concave up. How did you manage this? What does your graph look like? What does the integral function look like?
I could not get the derivative to make a concave up graph. The best I could get was a very spastic cancave up graph. I could not get it close to smooth. The integral was concave up, then flattens out at the top.
Now try to construct a graph whose integral is concave down. How did you manage this? What does your graph look like? What does the derivative function look like?
I made a concave down graph on f(x) that started below the horizontal axis. The derivative was mostly random with mesa like structure at the end
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Good.
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