Power Maths
This is an exercise devised by Sidney Schuman to help maths students find the calculus power rules numerically

For your chosen power and point location enter values of A, B, C and x in this table Repeat this routine for all the other powers

Confirm that equations A/B = n and x/c = n are true for graphs of y = x^{ n} (n = 2, 3, 4, 5) Assume that this holds for all values of x and n


Use A/B = n to deduce the Integral Power Rule Hint: The area of the rectangle is both a sum and a product


Use x/c = n to deduce the Differential Power Rule Hint: The gradient of the curve and its tangent are equal

Grateful thanks to David A Smith for his encouragement and to Lana Holden for the Java applet