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# Differential calculus: power functions

TLF ID L7822

Observe the non-linear graphs of various power functions (such as f(x) = x², or f(x) = x³) and select the expressions for finding the gradient of the secant between small changes in x represented by Δx. Tabulate the values of f'(x) and plot the derivative of each function. Determine the pattern between the graphs for each function. This learning object is one in a series of ten objects. Some objects in the series are also packaged as combined learning objects.

#### Educational details

Key learning objectives
• Students apply the concept of a limit in the context of the rate of change of a non-linear function.
• Students interpret the gradient of the tangent to a curve as being the rate of change of the function.
• Students apply first principles methods to differentiate the functions of various powers of x.
• Students interpret the concept of a derivative of a function, and identify the derivatives for various power functions of x.
• Students investigate the derivative to calculate the range of a function at a nominated point.
Educational value
• Introduces students to the language, notation and methods of differential calculus.
• Provides opportunities for students to find derivatives of functions from first principles.
• Allows students to construct tables for the derivatives of functions and plot the graphs.
• Summarises key statements related to difference quotients, derivatives and power functions.
• Displays feedback for correct and incorrect answers.
Year level

11; 12

Learning area
• mathematics
Strand
• Mathematics/Algebra
Student activity
• Interactives;
• Experiment;
• Analysis;
• Modelling;
• Multiple choice questions

#### Other details

Contributors
• Script writer
• Educational validator
• Name: Professor Graham Jones
• Technical implementer
• Subject matter expert
• Name: Howard Reeves
• Address: Lindisfarne TAS 7015 Australia
• Educational validator
• Name: Doctor Paul White
• Address: Strathfield NSW 2135 Australia
• Publisher
• Date of contribution: 20 Sep 2013
• Organisation: Education Services Australia
• Address: Melbourne VIC 3000 Australia
• URL: http://www.esa.edu.au/
Access profile
• Hearing independence
• Generic
Learning resource type
• Interactive Resource
Browsers
• Microsoft Internet Explorer - minimum version: 6.0 (MS-Windows) - maximum version: 7.0 (MS-Windows)
• Firefox - minimum version: 2.0 (MS-Windows)
• Safari - minimum version: 2.0 (MacOS)
Operating systems
• MacOS - minimum version: X
• MS-Windows - minimum version: 2000 - maximum version: XP
Rights
• © Education Services Australia Ltd, 2013, except where indicated under Acknowledgements.

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