Also, the f( a) and s( a) may be interchanged.) (Notice that there is no x in this expression t is the variable. Since our segment is vertical the first coordinate will have a = c and will reduce to a. The a, b, c, and d may be numbers or functions. In general, a segment from ( a, b) to ( c, d) is entered as the parametric/vector function Desmos does not have a segment operation, but here is how you graph a segment. In order to closely compare the function and its derivative, on the next line enter the equation of a vertical segment from a point on the function ( a, f( a)) to a point on the derivative ( a, s( a)). If so, you will have to change this line each time you change the function.
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Of course, you could enter the derivative here if your class has learned how to calculate derivatives. This will graph the derivative without having to calculate the derivative. Instead of a variable h, as we did in our last post in this series, enter 0.001. On the second line enter the symmetric difference quotient as Later you will be able to change this to other functions and investigate them, without changing anything else. Call it f( x) that is enter f( x) = your function. In the first entry line on the left, enter the equation of the function whose graph you want to explore.
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Open Desmos and sign into your account if you don’t have one then register – its free and you can keep your results and even share them with others. Hopefully, you and your students will soon be able to make your own to show exactly what you want. One of the things I have found over the years is that it takes some mathematical knowledge to make good demonstration graph and that in itself if useful and instructive.
Instead of presenting you with a completed Desmos graph, I will show you how to make you own. CAS calculators also have sliders but they are not as easy to use as Desmos. Desmos does this a lot better than graphing calculators, because of the easy use of sliders. Today I will show you how you can do this first with Desmos a free online graphing program and then on a graphing calculator. The fourth in the Graphing Calculator / Technology seriesĬomparing the graph of a function and its derivative is instructive and necessary in beginning calculus.