In today's blog, we look at the topic of Rates of change. With linear functions (straight line graphs) the rate of change can be interpreted from the gradient of the function. It is interpreted as an amount of y per amount of x (e.g. Dollars per hour, Metres per second). When dealing with non-linear functions there are two rates of change you could calculate.
The average rate of change; here you create a chord between two intervals and then calculate the gradient of the cord and interpret as a rate of change. The disadvantage of this is that it doesn't truly reflect the nature of the graph.
The other rate of change is an instantaneous rate of change; here you are working out the rate of change at a specific point. Create a tangent at the point, calculate and interpret the gradient as a rate of change. This will give a more accurate representation of what is happening but more tangents will be required to deliver the bigger picture.