Finding the gradient of a
applet beneath was created in GeoGebra, which is a small, free piece of
software that can be downloaded from: www.geogebra.org
Check the boxes to show the various features, and
move the point around to observe how the gradient changes.
By selecting 'Show tangent' you can see clearly how the gradient of the curve changes.
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
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.