# Derivative Curve from Function Curve

Taught by TheMathDude
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Part of video series
Meets NCTM Standards:
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.

Check out www.themathdude.org for more videos.

• 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.