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.


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.


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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