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# Differential calculus: derivatives graphing tool

TLF ID L7825

Use this revision tool to examine the relationship between functions and their derivatives by observing their graphs. Select a polynomial function (for example, f(x) = x³ – 3x²) from the menu. Estimate the gradients of the given tangents and position them on the graph of the function. Draw the graph of the derivative function. Use the slider to compare the values of the polynomial function and the derivative function. Complete the tasks for each polynomial function in the menu to continue exploring the visual relationship between the two graphs. This learning object is one in a series of ten objects.

#### Educational details

Key learning objectives
• Students interpret the gradient of the tangent to a curve as being the rate of change of the function.
• Students apply the first principles method to differentiate basic polynomial functions.
Educational value
• Encourages students to establish visual links between the graphs of polynomial functions and the graphs of their derivatives.
• Allows students to revise the key points related to functions and derivatives of functions.
• Requires students to estimate the gradients of tangents at given points on a curve.
• Automatically plots the points for the derivatives of the functions.
• Includes graphs for three polynomial functions and their derivatives.
Year level

11; 12

Learning area
• mathematics
Strand
• Mathematics/Algebra
Student activity
• Interactives;
• Experiment;
• Analysis;
• Modelling;
• Estimation

#### Other details

Contributors
• Script writer
• Subject matter expert
• Name: Howard Reeves
• Address: Lindisfarne TAS 7015 Australia
• Educational validator
• Name: Professor Graham Jones
• Educational validator
• Name: Doctor Paul White
• Address: Strathfield NSW 2135 Australia
• Technical implementer
• Publisher
• Date of contribution: 20 Sep 2013
• Organisation: Education Services Australia
• Address: Melbourne VIC 3000 Australia
• URL: http://www.esa.edu.au/
Access profile
• Colour independence
• Device independence
• Hearing independence
• Generic
Learning resource type
• Interactive Resource
Browsers
• Microsoft Internet Explorer - minimum version: 8.0 (MS-Windows) - maximum version: 9.0 (MS-Windows)
• Firefox - minimum version: (MS-Windows)
• Safari - minimum version: 5.1 (MacOS)
Operating systems
• MacOS - minimum version: 10.6
• MS-Windows - minimum version: XP - maximum version: 7
Rights
• © Education Services Australia Ltd, 2013, except where indicated under Acknowledgements.