Derivative Curve from Function Curve
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.
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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- 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
- 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?
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Staff Review
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.
