Gradient, Average and Instantaneous Rate of Change

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. [math]\frac{Change\;in\;y}{Change\;in\;x}[/math] 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)

 

Lew W.S.

 
Resource Type
Activity
Tags
average  change  derivative  difference-and-slope  exploration  gradient  instantaneous  rate  tangent 
Target Group (Age)
15 – 18
Language
English (United Kingdom)
 
 
GeoGebra version
4.2
Views
7771
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