Instantaneous rate of change

[Eboci]

Hello,

Given a graph how would you go about finding the instanteous rate of change at a point? I was thinking of drawing a tangent line, but there must be a more accurate way of doing it. Since no function of the graph is given, it is impossible to take any derivatives.

Thanks for the help
Eboci

 

[pka]

Given a graph how would you go about finding the instanteous rate of change at a point? I was thinking of drawing a tangent line, but there must be a more accurate way of doing it.

The best one can hope for is a good approximation. Drawing a tangent line and finding the slope of that tangent is the derivative at the point. Here is another way: use a series of approximations for the secants with one end point at the point. Make the secants ever shorter.