Power Maths

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

Links

 

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