# Differentiating powers of x (polynomials)

###### Author and programmer: Ron Barrow

This applet investigates differential calculus of powers of x (polynomials). You can plot the primary function ( ƒ(x) ), its first derivative (differential, the gradient function) ( ƒ'(x) ) and its second derivative ( ƒ''(x), the gradient of the gradient ) side by side for comparison. Use the applet to investigate increasing and decreasing functions, maximum, minimum and other turning points. See how the first and second differentials vary with the primary function.

UK Years 12-13, KS5, KS4, Core 1 (C1) GCE Mathematics, Algebra and Functions

US - Grades 11 - 12

Instructions below See also: Integrating Polynomials

## How to Use this Applet

This applet has several new features. The values of A, B, C, D, E and F are changed using the drag-boxes at the bottom. Just click in a box and drag left or right to change the value in the box. The x- and y-scales are changed using the two boxes at the bottom-right. You can also move the origin (0,0) by clicking the little circle there and dragging. Varying the values A-F changes the primary curve ( ƒ(x) ), and this in turn changes the first differential curve ( ƒ'(x) ) and the second differential curve ( ƒ''(x) ). You can turn any of these curves and functions off by unchecking the boxes at the top. Clicking reset sets up the start position again.

You can learn a great deal by playing around with this applet.