Introduction to Calculus
Finding the gradient of a curve 

The applet beneath was created in GeoGebra, which is a small, free piece of dynamic geometry software that can be downloaded from:

Calculus applet

Check the boxes to show the various features, and move the point around to observe how the gradient changes.  

This is a Java Applet created using GeoGebra from - it looks like you don't have Java installed, please go to
By selecting 'Show tangent' you can see clearly how the gradient of the curve changes.  
By selecting 'Show segment' you can compare this tangent line to a segment between two points on the curve.  The closer you bring these two points, the closer the segment between them becomes to the tangent line.  
By selecting 'Show gradient function' you can see what the graph of the gradient would look like - for negative gradients, it is below the x-axis, and at stationary points (where the gradient is zero) it is on the x-axis.