This is an exercise to help you spot the relationship between the shape of a curve and the shape of the gradient function for that curve.
  1. As you click and drag the green point along the curve, the gradient of the tangent "m" is shown. Draw up a table of values showing the x-coordinate of the point in one column and the gradient at that point in another column.
  2. Edit f(x) to give a different curve and repeat the drawing up of a table of values in (1) above. Don't forget to record your function f(x).
  3. If you click on point A1 in the left hand side (algebra) and now drag the green point around, a trace-plot of the gradient values will be drawn. Look at this and describe the family of curves that the trace-plot belongs to.
  4. Repeat this for several different functions - two or three straight lines, two or three quadratics and two or three cubic functions. What conclusions can you draw?