Introduction
to Calculus

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

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: 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.

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.

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.