Power Maths

Go straight to the calculus power rules

Try Sidney Schuman's pre-calculus exercise (disclaimer) and read his published articles

 

 

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 the equations  A/B = n  and  x/c = n

are both 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