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
- 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.)
- 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.
- 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.
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Here are the derivatives of the 3 functions given above:
1. Quadratic (parabola), `y=x^2-10x-1`.
2. Cubic, `y=0.015x^3-0.25x^2+0.49x+0.47`.
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.
Graph developed using JSXGraph.