Power Maths is a pre-calculus investigation designed to enable students to discover the integral and differential power rules numerically. The investigation leads the student to conjecture a simple ratio of areas, from which the rules are then deduced for the restricted domain [0,x].
Start the investigation in a new window.
A hardcopy version of Power Maths includes calculator/graph-based investigations for both power rules. If you would like a copy, or if you have any comments, please click the Worksheet link on the Investigation page.
Power Maths (both parts) appeared originally as a booklet used while teaching at Lewisham College, London UK.
Editor's note, 11/04: When published, this investigation included only the integral power rule, and there was a separate investigation for the differential power rule. The author has since combined these in the present version.
Acknowledgements: Grateful thanks to David A. Smith for his encouragement and to Lana Holden for the applet.