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.- 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.
- 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).
- 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.
- 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?
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