Understanding the Derivative of a Function

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This Demonstration explores the derivative of a single-variable continuous function at a point , relating it to the slope of the secant line that connects points and on the graph of the function.

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Use the first two sliders to position points and on the displayed function (black curve). Check the boxes "dashed lines " and "dashed lines " to better visualize the coordinates of the respective points. Check the box "secant " to display the secant line that connects points and , and check the box "tangent at " to display the tangent line at the current location of . Check the box "triangle" to visualize the increments and shown in the yellow portion of the table. Choose the function you want to work with by selecting a number from the available list under "choose "; check the box "show structure of " if you want to see the functional form of the displayed function.

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Contributed by: Whasington Silvestre (January 2024)
(Murray State University, Austin Peay State University, University of Puerto Rico, Autonomous University of Santo Domingo)
Open content licensed under CC BY-NC-SA


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