Derivative Curve from Function Curve

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Taught by TheMathDude
  • Currently 5.0/5 Stars.
3442 views | 1 rating
Meets NCTM Standards:
Lesson Summary:

In this lesson, you will learn how to construct or identify a Cartesian graph of the derivative of a function given the Cartesian graph of the function or vice versa. Using a Java program, the instructor demonstrates how to plot the slope of the tangent line at a particular input on the same graph as the original function to create a new function, the derivative curve. Through this process, students will learn about horizontal tangents, inflection points, and how to determine whether a derivative curve has a maximum or minimum value. By the end of the lesson, students will be able to sketch a rough derivative curve by hand or use technology to generate an accurate one.

Lesson Description:

Be able to construct or identify a Cartesian graph of the derivative of a function given the Cartesian graph of the function or vice versa.

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Additional Resources:
  • Derivative Function Applet - Java Applet that can help you see how the slope of the tangent at every input on a function can be itself be a new output of a new function which is the derivative of the given function
  • Derivative as the Slope of the Tangent - Java Applet that can help you see how the slope of the tangent at every input on a function can be itself be a new output of a new function which is the derivative of the given function
  • Function and Derivative Graphs Exercise - Drawing a derivative graph from a function and vice versa -- 2 example graphs are in this problem set
Questions answered by this video:
  • How can you draw the graph of the derivative of a function if you are given the graph of the initial function?
  • How do you find the slope of a function at every point along its curve?
  • What does the derivative of a cubic function look like?
  • Why is the derivative of a cubic function a quadratic function?
  • What is the relationship between the graph of a function and the graph of its derivative?
  • How do you know where the graph of a derivative function passes through 0, has a minimum or maximum, and is increasing or decreasing?
  • Can multiple functions all have the same derivative curve?
  • Staff Review

    • Currently 5.0/5 Stars.
    This lesson shows how to take the graph of a function and draw the graph of its derivative. This is done by plotting the slope of the function at many different points and then connecting them in a curve. The concepts behind the process of drawing the derivative function are explained very well. One derivative graph is drawn with a java applet and the next is drawn by hand.