This applet lets you investigate the gradient of a straight line, [br]or gradient of the tangent at a point on a curve of a function.[br][br]The rate of change of y with respect to x between two points [br]is the change in y divided by the change in x ie.[math]\frac{Change\;in\;y}{Change\;in\;x}[/math] [br][br]For the straight line you will note that the gradient is constant throughout the line, between points P & Q.[br][br]For the curve, gradient of a point C between points P & Q changes (vary) as the point C is moved. [br][br]The "average gradient" is the gradient of a straight line joining P & Q.[br][br]The instantaneous rate of change at P, is the gradient (rate of change)at which the change in x is made very very small[br] (ie by moving point Q towards P)

Observe the gradient of a straight line.[br]Click on the relevant checkboxes and move point Q by dragging with mouse cursor (left button pressed down)[br]1. Is the gradient constant along the line between P & Q?[br][br]Use the curved function graph instead of the straight line (Select the relevant checkbox)[br]2. Is the gradient constant along the line between P & Q[br][br]Click on the instantaneous rate of change checkbox and move point Q (or C) and see how the instantaneous rate of change at a point[br]is related to the gradient of curve at a point.