Gradient, Average and Instantaneous Rate of Change

Author:
Lew W.S.
This applet lets you investigate the gradient of a straight line, or gradient of the tangent at a point on a curve of a function. The rate of change of y with respect to x between two points is the change in y divided by the change in x ie. For the straight line you will note that the gradient is constant throughout the line, between points P & Q. For the curve, gradient of a point C between points P & Q changes (vary) as the point C is moved. The "average gradient" is the gradient of a straight line joining P & Q. The instantaneous rate of change at P, is the gradient (rate of change)at which the change in x is made very very small (ie by moving point Q towards P)
Observe the gradient of a straight line. Click on the relevant checkboxes and move point Q by dragging with mouse cursor (left button pressed down) 1. Is the gradient constant along the line between P & Q? Use the curved function graph instead of the straight line (Select the relevant checkbox) 2. Is the gradient constant along the line between P & Q 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 is related to the gradient of curve at a point.