# Derivatives Graphs

by M. Bourne

## Interactive Graph showing Differentiation of a Polynomial Function

In the following interactive you can explore how the slope of a curve changes as the variable x changes.

### Things to do

1. Drag the point P left and right to see how the slope of the tangent varies as x varies. (Keep your mouse cursor over the graph. A left-right motion works better than up-down.)
2. Select the "show the graph of derivative" which gives you the derivative function. Then once again, drag point P left and right and observe how the 2 curves are related.
3. Choose one of the other 2 curves and explore its slope.

The height of the right triangle (with P at one vertex) indicates the slope. It has a base of 1 unit.

## Background

Here are the derivatives of the 3 functions given above:

1. Quadratic (parabola), y=x^2-10x-1.

Derivative: dy/dx=2x-10

2. Cubic, y=0.015x^3-0.25x^2+0.49x+0.47.

Derivative: dy/dx=0.045x^2-0.5x+0.49

3. Quartic y=x^4-1.5x^3-6x^2+3.5x+3.

Derivative: dy/dx= 4x^3-4.5x^2-12x+3.5

See how to find these derivatives in the Derivatives of Polynomials section.

### Credits

Graph developed using JSXGraph.

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